Volume
LIPIcs, Volume 4
IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science
Event
FSTTCS 2009, December 15-17, 2009, Kanpur, IndiaEditors
Publication Details
- published at: 2009-12-07
- Publisher: Schloss Dagstuhl – Leibniz-Zentrum für Informatik
- ISBN: 978-3-939897-13-2
- DBLP: db/conf/fsttcs/fsttcs2009
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Complete Volume
LIPIcs, Volume 4, FSTTCS'09, Complete Volume
Abstract
LIPIcs, Volume 4, FSTTCS'09, Complete Volume
Cite as
IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 4, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2013)
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@Proceedings{kannan_et_al:LIPIcs.FSTTCS.2009,
title = {{LIPIcs, Volume 4, FSTTCS'09, Complete Volume}},
booktitle = {IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-13-2},
ISSN = {1868-8969},
year = {2013},
volume = {4},
editor = {Kannan, Ravi and Narayan Kumar, K.},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2009},
URN = {urn:nbn:de:0030-drops-40987},
doi = {10.4230/LIPIcs.FSTTCS.2009},
annote = {Keywords: LIPIcs, Volume 4, FSTTCS'09, Complete Volume}
}
Document
Front Matter
Preface -- IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (2009)
Abstract
This volume contains the proceedings of the 29th international conference on the Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2009), organized under the auspices of the Indian Association for Research in Computing Science (IARCS) at the Indian Institute of Technology, Kanpur, India.
Cite as
IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 4, pp. i-vii, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2009)
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@InProceedings{kannan_et_al:LIPIcs.FSTTCS.2009.2341,
author = {Kannan, Ravi and Narayan Kumar, K.},
title = {{Preface -- IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (2009)}},
booktitle = {IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science},
pages = {i--vii},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-13-2},
ISSN = {1868-8969},
year = {2009},
volume = {4},
editor = {Kannan, Ravi and Narayan Kumar, K.},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2009.2341},
URN = {urn:nbn:de:0030-drops-23415},
doi = {10.4230/LIPIcs.FSTTCS.2009.2341},
annote = {Keywords: Preface, proceedings, FSTTCS, referees, programme committee, organising committee}
}
Document
Mediating for Reduction (on Minimizing Alternating Büchi Automata)
Abstract
We propose a new approach for minimizing alternating B\"uchi automata (ABA). The approach is based on the so called \emph{mediated equivalence} on states of ABA, which is the maximal equivalence contained in the so called \emph{mediated preorder}. Two states $p$ and $q$ can be related by the mediated preorder if there is a~\emph{mediator} (mediating state) which forward simulates $p$ and backward simulates $q$. Under some further conditions, letting a computation on some word jump from $q$ to $p$ (due to they get collapsed) preserves the language as the automaton can anyway already accept the word without jumps by runs through the mediator. We further show how the mediated equivalence can be computed efficiently. Finally, we show that, compared to the standard forward simulation equivalence, the mediated equivalence can yield much more significant reductions when applied within the process of complementing B\"uchi automata where ABA are used as an intermediate model.
Cite as
Parosh A. Abdulla, Yu-Fang Chen, Lukas Holik, and Tomas Vojnar. Mediating for Reduction (on Minimizing Alternating Büchi Automata). In IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 4, pp. 1-12, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2009)
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@InProceedings{abdulla_et_al:LIPIcs.FSTTCS.2009.2302,
author = {Abdulla, Parosh A. and Chen, Yu-Fang and Holik, Lukas and Vojnar, Tomas},
title = {{Mediating for Reduction (on Minimizing Alternating B\"{u}chi Automata)}},
booktitle = {IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science},
pages = {1--12},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-13-2},
ISSN = {1868-8969},
year = {2009},
volume = {4},
editor = {Kannan, Ravi and Narayan Kumar, K.},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2009.2302},
URN = {urn:nbn:de:0030-drops-23027},
doi = {10.4230/LIPIcs.FSTTCS.2009.2302},
annote = {Keywords: Alternating Automata, Buchi Automata, Automata Minimization, Buchi Automata Complementation, Simulation Preorder, forward and backward simulation, mediated equivalence}
}
Document
Algorithms for Message Ferrying on Mobile ad hoc Networks
Abstract
Message Ferrying is a mobility assisted technique for working around the disconnectedness and sparsity of Mobile ad hoc networks. One of the importantquestions which arise in this context is to determine the routing of the ferry,so as to minimize the buffers used to store data at the nodes in thenetwork. We introduce a simple model to capture the ferry routingproblem. We characterize {\em stable} solutions of the system andprovide efficient approximation algorithms for the {\sc Min-Max
Buffer Problem} for the case when the nodes are onhierarchically separated metric spaces.
Cite as
Mostafa Ammar, Deeparnab Chakrabarty, Atish Das Sarma, Subrahmanyam Kalyanasundaram, and Richard J. Lipton. Algorithms for Message Ferrying on Mobile ad hoc Networks. In IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 4, pp. 13-24, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2009)
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@InProceedings{ammar_et_al:LIPIcs.FSTTCS.2009.2303,
author = {Ammar, Mostafa and Chakrabarty, Deeparnab and Sarma, Atish Das and Kalyanasundaram, Subrahmanyam and Lipton, Richard J.},
title = {{Algorithms for Message Ferrying on Mobile ad hoc Networks}},
booktitle = {IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science},
pages = {13--24},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-13-2},
ISSN = {1868-8969},
year = {2009},
volume = {4},
editor = {Kannan, Ravi and Narayan Kumar, K.},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2009.2303},
URN = {urn:nbn:de:0030-drops-23031},
doi = {10.4230/LIPIcs.FSTTCS.2009.2303},
annote = {Keywords: Algorithms, Network Algorithms, Routing, TSP, Buffer Optimization}
}
Document
Arithmetic Circuits and the Hadamard Product of Polynomials
Abstract
Motivated by the Hadamard product of matrices we define the Hadamard
product of multivariate polynomials and study its arithmetic circuit
and branching program complexity. We also give applications and
connections to polynomial identity testing. Our main results are
the following.
\begin{itemize}
\item[$\bullet$] We show that noncommutative polynomial identity testing for
algebraic branching programs over rationals is complete for
the logspace counting class $\ceql$, and over fields of characteristic
$p$ the problem is in $\ModpL/\Poly$.
\item[$\bullet$] We show an exponential lower bound for expressing the
Raz-Yehudayoff polynomial as the Hadamard product of two monotone
multilinear polynomials. In contrast the Permanent can be expressed
as the Hadamard product of two monotone multilinear formulas of
quadratic size.
\end{itemize}
Cite as
Vikraman Arvind, Pushkar S. Joglekar, and Srikanth Srinivasan. Arithmetic Circuits and the Hadamard Product of Polynomials. In IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 4, pp. 25-36, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2009)
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@InProceedings{arvind_et_al:LIPIcs.FSTTCS.2009.2304,
author = {Arvind, Vikraman and Joglekar, Pushkar S. and Srinivasan, Srikanth},
title = {{Arithmetic Circuits and the Hadamard Product of Polynomials}},
booktitle = {IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science},
pages = {25--36},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-13-2},
ISSN = {1868-8969},
year = {2009},
volume = {4},
editor = {Kannan, Ravi and Narayan Kumar, K.},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2009.2304},
URN = {urn:nbn:de:0030-drops-23046},
doi = {10.4230/LIPIcs.FSTTCS.2009.2304},
annote = {Keywords: Hadamard product, identity testing, lower bounds, algebraic branching programs}
}
Document
Kernels for Feedback Arc Set In Tournaments
Abstract
A tournament $T = (V,A)$ is a directed graph in which there is exactly one arc between every pair of distinct vertices. Given a digraph on $n$ vertices and an integer parameter $k$, the {\sc Feedback Arc Set} problem asks whether thegiven digraph has a set of $k$ arcs whose removal results in an acyclicdigraph. The {\sc Feedback Arc Set} problem restricted to tournaments is knownas the {\sc $k$-Feedback Arc Set in Tournaments ($k$-FAST)} problem. In thispaper we obtain a linear vertex kernel for \FAST{}. That is, we give apolynomial time algorithm which given an input instance $T$ to \FAST{} obtains an equivalent instance $T'$ on $O(k)$ vertices. In fact, given any fixed $\epsilon > 0$, the kernelized instance has at most $(2 + \epsilon)k$ vertices.Our result improves the previous known bound of $O(k^2)$ on the kernel size for\FAST{}. Our kernelization algorithm solves the problem on a subclass of
tournaments in polynomial time and uses a known polynomial time approximation
scheme for \FAST.
Cite as
Stéphane Bessy, Fedor V. Fomin, Serge Gaspers, Christophe Paul, Anthony Perez, Saket Saurabh, and Stéphan Thomassé. Kernels for Feedback Arc Set In Tournaments. In IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 4, pp. 37-47, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2009)
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@InProceedings{bessy_et_al:LIPIcs.FSTTCS.2009.2305,
author = {Bessy, St\'{e}phane and Fomin, Fedor V. and Gaspers, Serge and Paul, Christophe and Perez, Anthony and Saurabh, Saket and Thomass\'{e}, St\'{e}phan},
title = {{Kernels for Feedback Arc Set In Tournaments}},
booktitle = {IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science},
pages = {37--47},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-13-2},
ISSN = {1868-8969},
year = {2009},
volume = {4},
editor = {Kannan, Ravi and Narayan Kumar, K.},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2009.2305},
URN = {urn:nbn:de:0030-drops-23055},
doi = {10.4230/LIPIcs.FSTTCS.2009.2305},
annote = {Keywords: Parameterized complexity, kernels, tournaments}
}
Document
On the Memory Consumption of Probabilistic Pushdown Automata
Abstract
We investigate the problem of evaluating memory consumption for systems modelled by probabilistic pushdown automata (pPDA). The space needed by a runof a pPDA is the maximal height reached by the stack during the run. Theproblem is motivated by the investigation of depth-first computations that playan important role for space-efficient schedulings of multithreaded programs.
We study the computation of both the distribution of the memory consumption and its expectation. For the distribution, we show that a naive method incurs anexponential blow-up, and that it can be avoided using linear equation systems.We also suggest a possibly even faster approximation method.Given~$\varepsilon>0$, these methods allow to compute bounds on the memoryconsumption that are exceeded with a probability of at most~$\varepsilon$.
For the expected memory consumption, we show that whether it is infinite can be decided in polynomial time for stateless pPDA (pBPA) and in polynomial space for pPDA. We also provide an iterative method for approximating theexpectation. We show how to compute error bounds of our approximation methodand analyze its convergence speed. We prove that our method convergeslinearly, i.e., the number of accurate bits of the approximation is a linear function of the number of iterations.
Cite as
Tomas Brazdil, Javier Esparza, and Stefan Kiefer. On the Memory Consumption of Probabilistic Pushdown Automata. In IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 4, pp. 49-60, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2009)
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@InProceedings{brazdil_et_al:LIPIcs.FSTTCS.2009.2306,
author = {Brazdil, Tomas and Esparza, Javier and Kiefer, Stefan},
title = {{On the Memory Consumption of Probabilistic Pushdown Automata}},
booktitle = {IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science},
pages = {49--60},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-13-2},
ISSN = {1868-8969},
year = {2009},
volume = {4},
editor = {Kannan, Ravi and Narayan Kumar, K.},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2009.2306},
URN = {urn:nbn:de:0030-drops-23067},
doi = {10.4230/LIPIcs.FSTTCS.2009.2306},
annote = {Keywords: Pushdown automata, probabilistic systems, verification}
}
Document
Continuous-Time Stochastic Games with Time-Bounded Reachability
Abstract
We study continuous-time stochastic games with time-bounded
reachability objectives. We show that each vertex in such a game
has a \emph{value} (i.e., an equilibrium probability), and we
classify the conditions under which optimal strategies exist.
Finally, we show how to compute optimal strategies in finite uniform
games, and how to compute $\varepsilon$-optimal strategies in
finitely-branching games with bounded rates (for finite games, we
provide detailed complexity estimations).
Cite as
Tomas Brazdil, Vojtech Forejt, Jan Krcal, Jan Kretinsky, and Antonin Kucera. Continuous-Time Stochastic Games with Time-Bounded Reachability. In IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 4, pp. 61-72, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2009)
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@InProceedings{brazdil_et_al:LIPIcs.FSTTCS.2009.2307,
author = {Brazdil, Tomas and Forejt, Vojtech and Krcal, Jan and Kretinsky, Jan and Kucera, Antonin},
title = {{Continuous-Time Stochastic Games with Time-Bounded Reachability}},
booktitle = {IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science},
pages = {61--72},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-13-2},
ISSN = {1868-8969},
year = {2009},
volume = {4},
editor = {Kannan, Ravi and Narayan Kumar, K.},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2009.2307},
URN = {urn:nbn:de:0030-drops-23077},
doi = {10.4230/LIPIcs.FSTTCS.2009.2307},
annote = {Keywords: Continuous time stochastic systems, time bounded reachability, stochastic games}
}
Document
Deterministic Automata and Extensions of Weak MSO
Abstract
We introduce a new class of automata on infinite words, called
min-automata. We prove that min-automata have the same expressive
power as weak monadic second-order logic (weak MSO) extended with a new
quantifier, the recurrence quantifier. These results are dual to a
framework presented in \cite{max-automata}, where max-automata were proved equivalent
to weak MSO extended with an unbounding
quantifier. We also present a general framework, which tries to
explain which types of automata on infinite words correspond to
extensions of weak MSO. As another example for the usefulness framework,
apart from min- and max-automata, we define an extension of weak MSO
with a quantifier that talks about ultimately periodic sets.
Cite as
Mikolaj Bojanczyk and Szymon Torunczyk. Deterministic Automata and Extensions of Weak MSO. In IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 4, pp. 73-84, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2009)
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@InProceedings{bojanczyk_et_al:LIPIcs.FSTTCS.2009.2308,
author = {Bojanczyk, Mikolaj and Torunczyk, Szymon},
title = {{Deterministic Automata and Extensions of Weak MSO}},
booktitle = {IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science},
pages = {73--84},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-13-2},
ISSN = {1868-8969},
year = {2009},
volume = {4},
editor = {Kannan, Ravi and Narayan Kumar, K.},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2009.2308},
URN = {urn:nbn:de:0030-drops-23081},
doi = {10.4230/LIPIcs.FSTTCS.2009.2308},
annote = {Keywords: Deterministic automata, Weak MSO, min-automata, max-automata, BS-automata}
}
Document
On Timed Alternating Simulation for Concurrent Timed Games
Abstract
We address the problem of alternating simulation refinement for concurrent timed games (\TG). We show that checking timed alternating simulation between\TG is \EXPTIME-complete, and provide a logical characterization of thispreorder in terms of a meaningful fragment of a new logic, \TAMTLSTAR.\TAMTLSTAR is an action-based timed extension of standard alternating-timetemporal logic \ATLSTAR, which allows to quantify on strategies where thedesignated player is not responsible for blocking time. While for full
\TAMTLSTAR, model-checking \TG is undecidable, we show that for its fragment
\TAMTL, corresponding to the timed version of \ATL, in \EXPTIME.
Cite as
Laura Bozzelli, Axel Legay, and Sophie Pinchinat. On Timed Alternating Simulation for Concurrent Timed Games. In IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 4, pp. 85-96, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2009)
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@InProceedings{bozzelli_et_al:LIPIcs.FSTTCS.2009.2309,
author = {Bozzelli, Laura and Legay, Axel and Pinchinat, Sophie},
title = {{On Timed Alternating Simulation for Concurrent Timed Games}},
booktitle = {IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science},
pages = {85--96},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-13-2},
ISSN = {1868-8969},
year = {2009},
volume = {4},
editor = {Kannan, Ravi and Narayan Kumar, K.},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2009.2309},
URN = {urn:nbn:de:0030-drops-23092},
doi = {10.4230/LIPIcs.FSTTCS.2009.2309},
annote = {Keywords: Concurrent Timed Games, Timed Alternating Simulation, Timed Alternating Temporal Logics}
}
Document
Covering of ordinals
Abstract
The paper focuses on the structure of fundamental sequences of
ordinals smaller than $\e$. A first result is the construction of a
monadic second-order formula identifying a given structure, whereas
such a formula cannot exist for ordinals themselves. The structures
are precisely classified in the pushdown hierarchy. Ordinals are also
located in the hierarchy, and a direct presentation is given.
Cite as
Laurent Braud. Covering of ordinals. In IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 4, pp. 97-108, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2009)
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@InProceedings{braud:LIPIcs.FSTTCS.2009.2310,
author = {Braud, Laurent},
title = {{Covering of ordinals}},
booktitle = {IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science},
pages = {97--108},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-13-2},
ISSN = {1868-8969},
year = {2009},
volume = {4},
editor = {Kannan, Ravi and Narayan Kumar, K.},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2009.2310},
URN = {urn:nbn:de:0030-drops-23108},
doi = {10.4230/LIPIcs.FSTTCS.2009.2310},
annote = {Keywords: Ordinal theory, pushdown hierarchy, fundamental sequence, monadic second-order logic, prefix-recognizable graphs}
}
Document
Fractional Pebbling and Thrifty Branching Programs
Abstract
We study the branching program complexity of the {\em tree evaluation problem},
introduced in \cite{BrCoMcSaWe09} as a candidate for separating \nl\ from\logcfl. The input to the problem is a rooted, balanced $d$-ary tree of height$h$, whose internal nodes are labelled with $d$-ary functions on$[k]=\{1,\ldots,k\}$, and whose leaves are labelled with elements of $[k]$.Each node obtains a value in $[k]$ equal to its $d$-ary function applied to the values of its $d$ children. The output is the value of the root.
Deterministic $k$-way branching programs as related to black pebbling algorithms have been studied in \cite{BrCoMcSaWe09}. Here we introduce the notion of {\em fractional pebbling} of graphs to study non-deterministicbranching program size. We prove that this yields non-deterministic branching
programs with $\Theta(k^{h/2+1})$ states solving the Boolean problem ``determine whether the root has value 1'' for binary trees - this isasymptotically better than the branching program size corresponding toblack-white pebbling. We prove upper and lower bounds on the fractionalpebbling number of $d$-ary trees, as well as a general result relating thefractional pebbling number of a graph to the black-white pebbling number.
We introduce a simple semantic restriction called {\em thrifty} on $k$-way branching programs solving tree evaluation problems and show that the branchingprogram size bound of $\Theta(k^h)$ is tight (up to a constant factor) for all
$h\ge 2$ for deterministic thrifty programs. We show that thenon-deterministic branching programs that correspond to fractional pebbling are
thrifty as well, and that the bound of $\Theta(k^{h/2+1})$ is tight for
non-deterministic thrifty programs for $h=2,3,4$. We hypothesise that thrifty
branching programs are optimal among $k$-way branching programs solving the
tree evaluation problem - proving this for deterministic programs would
separate \lspace\ from \logcfl\, and proving it for non-deterministic programs
would separate \nl\ from \logcfl.
Cite as
Mark Braverman, Stephen Cook, Pierre McKenzie, Rahul Santhanam, and Dustin Wehr. Fractional Pebbling and Thrifty Branching Programs. In IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 4, pp. 109-120, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2009)
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@InProceedings{braverman_et_al:LIPIcs.FSTTCS.2009.2311,
author = {Braverman, Mark and Cook, Stephen and McKenzie, Pierre and Santhanam, Rahul and Wehr, Dustin},
title = {{Fractional Pebbling and Thrifty Branching Programs}},
booktitle = {IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science},
pages = {109--120},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-13-2},
ISSN = {1868-8969},
year = {2009},
volume = {4},
editor = {Kannan, Ravi and Narayan Kumar, K.},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2009.2311},
URN = {urn:nbn:de:0030-drops-23111},
doi = {10.4230/LIPIcs.FSTTCS.2009.2311},
annote = {Keywords: Branching programs, space complexity, tree evaluation, pebbling}
}
Document
The Wadge Hierarchy of Max-Regular Languages
Abstract
Recently, Miko{\l}aj Boja{\'n}czyk introduced a class of max-regular languages, an extension of regular languages of infinite words preserving manyof its usual properties. This new class can be seen as a different way of generalising the notion of regularity from finite to infinite words. This paper compares regular and max-regular languages in terms of topological complexity.It is proved that up to Wadge equivalence the classes coincide. Moreover, when restricted to $\mathbf{\Delta}^0_2$-languages, the classes contain virtually the same languages. On the other hand, separating examples of arbitrary complexity exceeding $\mathbf{\Delta}^0_2$ are constructed.
Cite as
Jérémie Cabessa, Jacques Duparc, Alessandro Facchini, and Filip Murlak. The Wadge Hierarchy of Max-Regular Languages. In IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 4, pp. 121-132, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2009)
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@InProceedings{cabessa_et_al:LIPIcs.FSTTCS.2009.2312,
author = {Cabessa, J\'{e}r\'{e}mie and Duparc, Jacques and Facchini, Alessandro and Murlak, Filip},
title = {{The Wadge Hierarchy of Max-Regular Languages}},
booktitle = {IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science},
pages = {121--132},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-13-2},
ISSN = {1868-8969},
year = {2009},
volume = {4},
editor = {Kannan, Ravi and Narayan Kumar, K.},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2009.2312},
URN = {urn:nbn:de:0030-drops-23122},
doi = {10.4230/LIPIcs.FSTTCS.2009.2312},
annote = {Keywords: Max-regular languages, Wadge hierarchy, Wagner hierarchy}
}
Document
Automata and temporal logic over arbitrary linear time
Abstract
Linear temporal logic was introduced in order to reason about reactive
systems. It is often considered with respect to infinite words, to specify
the behaviour of long-running systems. One can consider more general models
for linear time, using words indexed by arbitrary linear orderings. We
investigate the connections between temporal logic and automata on linear
orderings, as introduced by Bruyere and Carton. We provide a doubly
exponential procedure to compute from any LTL formula with \until, \since, and
the Stavi connectives an automaton that decides whether that formula holds on
the input word. In particular, since the emptiness problem for these automata
is decidable, this transformation gives a decision procedure for the
satisfiability of the logic.
Cite as
Julien Cristau. Automata and temporal logic over arbitrary linear time. In IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 4, pp. 133-144, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2009)
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@InProceedings{cristau:LIPIcs.FSTTCS.2009.2313,
author = {Cristau, Julien},
title = {{Automata and temporal logic over arbitrary linear time}},
booktitle = {IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science},
pages = {133--144},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-13-2},
ISSN = {1868-8969},
year = {2009},
volume = {4},
editor = {Kannan, Ravi and Narayan Kumar, K.},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2009.2313},
URN = {urn:nbn:de:0030-drops-23132},
doi = {10.4230/LIPIcs.FSTTCS.2009.2313},
annote = {Keywords: LTL, linear orderings, automata}
}
Document
Graph Isomorphism for K_{3,3}-free and K_5-free graphs is in Log-space
Abstract
Graph isomorphism is an important and widely studied computational problem with
a yet unsettled complexity.
However, the exact complexity is known for isomorphism of various classes of
graphs. Recently, \cite{DLNTW09} proved that planar isomorphism is complete for log-space.
We extend this result %of \cite{DLNTW09}
further to the classes of graphs which exclude $K_{3,3}$ or $K_5$ as
a minor, and give a log-space algorithm.
Our algorithm decomposes $K_{3,3}$ minor-free graphs into biconnected and those further into triconnected
components, which are known to be either planar or $K_5$ components \cite{Vaz89}. This gives a triconnected
component tree similar to that for planar graphs. An extension of the log-space algorithm of \cite{DLNTW09}
can then be used to decide the isomorphism problem.
For $K_5$ minor-free graphs, we consider $3$-connected components.
These are either planar or isomorphic to the four-rung mobius ladder on $8$ vertices
or, with a further decomposition, one obtains planar $4$-connected components \cite{Khu88}.
We give an algorithm to get a unique
decomposition of $K_5$ minor-free graphs into bi-, tri- and $4$-connected components,
and construct trees, accordingly.
Since the algorithm of \cite{DLNTW09} does
not deal with four-connected component trees, it needs to be modified in a quite non-trivial way.
Cite as
Samir Datta, Prajakta Nimbhorkar, Thomas Thierauf, and Fabian Wagner. Graph Isomorphism for K_{3,3}-free and K_5-free graphs is in Log-space. In IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 4, pp. 145-156, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2009)
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@InProceedings{datta_et_al:LIPIcs.FSTTCS.2009.2314,
author = {Datta, Samir and Nimbhorkar, Prajakta and Thierauf, Thomas and Wagner, Fabian},
title = {{Graph Isomorphism for K\underline\{3,3\}-free and K\underline5-free graphs is in Log-space}},
booktitle = {IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science},
pages = {145--156},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-13-2},
ISSN = {1868-8969},
year = {2009},
volume = {4},
editor = {Kannan, Ravi and Narayan Kumar, K.},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2009.2314},
URN = {urn:nbn:de:0030-drops-23144},
doi = {10.4230/LIPIcs.FSTTCS.2009.2314},
annote = {Keywords: Graph isomorphism, K\underline\{3,3\}-free graphs, K\underline5-free graphs, log-space}
}
Document
Domination Problems in Nowhere-Dense Classes
Abstract
We investigate the parameterized complexity of generalisations and variations
of the dominating set problem on classes of graphs that are nowhere dense. In
particular, we show that the distance-$d$ dominating-set problem, also known
as the $(k,d)$-centres problem, is fixed-parameter tractable on any class that
is nowhere dense and closed under induced subgraphs. This generalises known
results about the dominating set problem on $H$-minor free classes, classes
with locally excluded minors and classes of graphs of bounded expansion. A
key feature of our proof is that it is based simply on the fact that these
graph classes are uniformly quasi-wide, and does not rely on a structural
decomposition. Our result also establishes that the distance-$d$
dominating-set problem is FPT on classes of bounded expansion, answering a
question of Ne{\v s}et{\v r}il and Ossona de Mendez.
Cite as
Anuj Dawar and Stephan Kreutzer. Domination Problems in Nowhere-Dense Classes. In IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 4, pp. 157-168, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2009)
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@InProceedings{dawar_et_al:LIPIcs.FSTTCS.2009.2315,
author = {Dawar, Anuj and Kreutzer, Stephan},
title = {{Domination Problems in Nowhere-Dense Classes}},
booktitle = {IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science},
pages = {157--168},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-13-2},
ISSN = {1868-8969},
year = {2009},
volume = {4},
editor = {Kannan, Ravi and Narayan Kumar, K.},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2009.2315},
URN = {urn:nbn:de:0030-drops-23153},
doi = {10.4230/LIPIcs.FSTTCS.2009.2315},
annote = {Keywords: Dominating Set, distance-d dominating set, nowhere-dense graph classes, H-minor free graphs, fixed-parameter tractablility}
}
Document
Simulation based security in the applied pi calculus
Abstract
We present a symbolic framework for refinement and composition of
security protocols. The framework uses the notion of ideal
functionalities. These are abstract systems which are secure by
construction and which can be combined into larger systems. They can
be separately refined in order to obtain concrete protocols
implementing them. Our work builds on ideas from the ``trusted
party paradigm'' used in computational cryptography models. The
underlying language we use is the applied pi calculus which is a
general language for specifying security protocols. In our framework
we can express the different standard flavours of simulation-based
security which happen to all coincide. We illustrate our framework
on an authentication functionality which can be realized using the
Needham-Schroeder-Lowe protocol. For this we need to define an
ideal functionality for asymmetric encryption and its
realization. We show a joint state result for this
functionality which allows composition (even though the same key
material is reused) using a tagging mechanism.
Cite as
Stéphanie Delaune, Steve Kremer, and Olivier Pereira. Simulation based security in the applied pi calculus. In IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 4, pp. 169-180, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2009)
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@InProceedings{delaune_et_al:LIPIcs.FSTTCS.2009.2316,
author = {Delaune, St\'{e}phanie and Kremer, Steve and Pereira, Olivier},
title = {{Simulation based security in the applied pi calculus}},
booktitle = {IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science},
pages = {169--180},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-13-2},
ISSN = {1868-8969},
year = {2009},
volume = {4},
editor = {Kannan, Ravi and Narayan Kumar, K.},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2009.2316},
URN = {urn:nbn:de:0030-drops-23163},
doi = {10.4230/LIPIcs.FSTTCS.2009.2316},
annote = {Keywords: Simulation based security, applied pi calculus, joint state theorem, authentication protocols}
}
Document
The Covering and Boundedness Problems for Branching Vector Addition Systems
Abstract
The covering and boundedness problems for
branching vector addition systems
are shown complete for doubly-exponential time.
Cite as
Stéphane Demri, Marcin Jurdzinski, Oded Lachish, and Ranko Lazic. The Covering and Boundedness Problems for Branching Vector Addition Systems. In IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 4, pp. 181-192, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2009)
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@InProceedings{demri_et_al:LIPIcs.FSTTCS.2009.2317,
author = {Demri, St\'{e}phane and Jurdzinski, Marcin and Lachish, Oded and Lazic, Ranko},
title = {{The Covering and Boundedness Problems for Branching Vector Addition Systems}},
booktitle = {IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science},
pages = {181--192},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-13-2},
ISSN = {1868-8969},
year = {2009},
volume = {4},
editor = {Kannan, Ravi and Narayan Kumar, K.},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2009.2317},
URN = {urn:nbn:de:0030-drops-23173},
doi = {10.4230/LIPIcs.FSTTCS.2009.2317},
annote = {Keywords: Vector addition systems, Petri nets, covering, boundedness, computational complexity}
}
Document
Subexponential Algorithms for Partial Cover Problems
Abstract
Partial Cover problems are optimization versions
of fundamental and well studied problems like {\sc Vertex Cover} and {\sc Dominating Set}.
Here one is interested in covering (or dominating) the maximum number of edges (or vertices) using a given number ($k$) of vertices, rather than covering all edges (or vertices). In general graphs, these problems are hard for parameterized complexity classes when parameterized by $k$.
It was recently shown by Amini et. al. [{\em FSTTCS 08}\,] that {\sc Partial Vertex Cover} and {\sc Partial Dominating Set} are fixed parameter tractable on large classes of sparse graphs, namely $H$-minor free graphs,
which include planar graphs and graphs of bounded genus. In particular, it was shown that on planar graphs both problems can be solved in time $2^{\cO(k)}n^{\cO(1)}$.
Cite as
Fedor V. Fomin, Daniel Lokshtanov, Venkatesh Raman, and Saket Saurabh. Subexponential Algorithms for Partial Cover Problems. In IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 4, pp. 193-201, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2009)
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@InProceedings{fomin_et_al:LIPIcs.FSTTCS.2009.2318,
author = {Fomin, Fedor V. and Lokshtanov, Daniel and Raman, Venkatesh and Saurabh, Saket},
title = {{Subexponential Algorithms for Partial Cover Problems}},
booktitle = {IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science},
pages = {193--201},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-13-2},
ISSN = {1868-8969},
year = {2009},
volume = {4},
editor = {Kannan, Ravi and Narayan Kumar, K.},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2009.2318},
URN = {urn:nbn:de:0030-drops-23186},
doi = {10.4230/LIPIcs.FSTTCS.2009.2318},
annote = {Keywords: Partial cover problems, parameterized complexity, subexponential time algorithms, irrelevant vertex technique}
}
Document
On the Tightening of the Standard SDP for Vertex Cover with $ell_1$ Inequalities
Abstract
We show that the integrality gap of the standard SDP for \vc~on instances of $n$ vertices remains $2-o(1)$ even after
the addition of \emph{all} hypermetric inequalities. Our lower bound requires new insights into the structure of SDP
solutions behaving like $\ell_1$ metric spaces when one point is removed. We also show that the addition of all
$\ell_1$ inequalities eliminates any solutions that are not convex combination of integral solutions. Consequently, we
provide the strongest possible separation between hypermetrics and $\ell_1$ inequalities with respect to the
tightening of the standard SDP for \vc.
Cite as
Konstantinos Georgiou, Avner Magen, and Iannis Tourlakis. On the Tightening of the Standard SDP for Vertex Cover with $ell_1$ Inequalities. In IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 4, pp. 203-214, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2009)
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@InProceedings{georgiou_et_al:LIPIcs.FSTTCS.2009.2319,
author = {Georgiou, Konstantinos and Magen, Avner and Tourlakis, Iannis},
title = {{On the Tightening of the Standard SDP for Vertex Cover with \$ell\underline1\$ Inequalities}},
booktitle = {IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science},
pages = {203--214},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-13-2},
ISSN = {1868-8969},
year = {2009},
volume = {4},
editor = {Kannan, Ravi and Narayan Kumar, K.},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2009.2319},
URN = {urn:nbn:de:0030-drops-23195},
doi = {10.4230/LIPIcs.FSTTCS.2009.2319},
annote = {Keywords: Semidefinite Programming, Vertex Cover, Integrality Gap, Hypermetric Inequalities}
}
Document
Kolmogorov Complexity in Randomness Extraction
Abstract
We clarify the role of Kolmogorov complexity in the area of randomness
extraction. We show that a computable function is an almost
randomness extractor if and only if it is a Kolmogorov complexity
extractor, thus establishing a fundamental equivalence between two
forms of extraction studied in the literature: Kolmogorov extraction
and randomness extraction. We present a distribution ${\cal M}_k$
based on Kolmogorov complexity that is complete for randomness
extraction in the sense that a computable function is an almost
randomness extractor if and only if it extracts randomness from ${\cal
M}_k$.
Cite as
John M. Hitchcock, Aduri Pavan, and N. V. Vinodchandran. Kolmogorov Complexity in Randomness Extraction. In IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 4, pp. 215-226, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2009)
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@InProceedings{hitchcock_et_al:LIPIcs.FSTTCS.2009.2320,
author = {Hitchcock, John M. and Pavan, Aduri and Vinodchandran, N. V.},
title = {{Kolmogorov Complexity in Randomness Extraction}},
booktitle = {IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science},
pages = {215--226},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-13-2},
ISSN = {1868-8969},
year = {2009},
volume = {4},
editor = {Kannan, Ravi and Narayan Kumar, K.},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2009.2320},
URN = {urn:nbn:de:0030-drops-23201},
doi = {10.4230/LIPIcs.FSTTCS.2009.2320},
annote = {Keywords: Extractors, Kolmogorov extractors, randomness}
}
Document
Donation Center Location Problem
Abstract
We introduce and study the {\em donation center location} problem, which
has an additional application in network
testing and may also be of independent interest as a general graph-theoreticproblem.Given a set of agents and a set of centers, where agents have preferences over centers and centers have capacities,
the goal is to open a subset of centers and to assign a maximum-sized subset of agents to their most-preferred
open centers, while respecting the capacity constraints.
We prove that in general, the problem
is hard to approximate within $n^{1/2-\epsilon}$ for any $\epsilon>0$.
In view of this, we investigate two special cases.
In one, every agent has a bounded number of centers on her preference list,
and in the other, all preferences are induced by a line-metric.
We present constant-factor approximation algorithms
for the former and exact polynomial-time algorithms for the latter.
Of particular interest among our techniques are an analysis of the greedy
algorithm for a variant of the maximum coverage problem called\emph{frugal coverage}, the use of maximum matching subroutine with subsequent
modification, analyzed using a counting argument, and a reduction to the independent set problem
on \emph{terminal intersection graphs}, which we show to be
a subclass of trapezoid graphs.
Cite as
Chien-Chung Huang and Zoya Svitkina. Donation Center Location Problem. In IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 4, pp. 227-238, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2009)
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@InProceedings{huang_et_al:LIPIcs.FSTTCS.2009.2321,
author = {Huang, Chien-Chung and Svitkina, Zoya},
title = {{Donation Center Location Problem}},
booktitle = {IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science},
pages = {227--238},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-13-2},
ISSN = {1868-8969},
year = {2009},
volume = {4},
editor = {Kannan, Ravi and Narayan Kumar, K.},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2009.2321},
URN = {urn:nbn:de:0030-drops-23212},
doi = {10.4230/LIPIcs.FSTTCS.2009.2321},
annote = {Keywords: Approximation Algorithms, Facility Location, Matching with Preferences}
}
Document
Non-Local Box Complexity and Secure Function Evaluation
Abstract
A non-local box is an abstract device into which Alice and Bob input bits $x$ and $y$ respectively and receive outputs $a$ and $b$ respectively, where $a,b$ are uniformly distributed and $a \oplus b = x \wedge y$. Such boxes have been central to the study of quantum or generalized non-locality as well as the simulation of non-signaling distributions. In this paper, we start by studying how many non-local boxes Alice and Bob need in order to compute a Boolean function $f$. We provide tight upper and lower bounds in terms of the communication complexity of the function both in the deterministic and randomized case. We show that non-local box complexity has interesting applications to classical cryptography, in particular to secure function evaluation, and study the question posed by Beimel and Malkin \cite{BM} of how many Oblivious Transfer calls Alice and Bob need in order to securely compute a function $f$. We show that this question is related to the non-local box complexity of the function and conclude by greatly improving their bounds. Finally, another consequence of our results is that traceless two-outcome
measurements on maximally entangled states can be simulated with 3 \nlbs, while
no finite bound was previously known.
Cite as
Marc Kaplan, Iordanis Kerenidis, Sophie Laplante, and Jérémie Roland. Non-Local Box Complexity and Secure Function Evaluation. In IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 4, pp. 239-250, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2009)
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@InProceedings{kaplan_et_al:LIPIcs.FSTTCS.2009.2322,
author = {Kaplan, Marc and Kerenidis, Iordanis and Laplante, Sophie and Roland, J\'{e}r\'{e}mie},
title = {{Non-Local Box Complexity and Secure Function Evaluation}},
booktitle = {IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science},
pages = {239--250},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-13-2},
ISSN = {1868-8969},
year = {2009},
volume = {4},
editor = {Kannan, Ravi and Narayan Kumar, K.},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2009.2322},
URN = {urn:nbn:de:0030-drops-23226},
doi = {10.4230/LIPIcs.FSTTCS.2009.2322},
annote = {Keywords: Communication complexity, non-locality, non-local boxes, secure function evaluation}
}
Document
Verification and Refutation of Probabilistic Specifications via Games
Abstract
We develop an abstraction-based framework
to check probabilistic specifications of Markov Decision Processes (MDPs) using
the stochastic two-player game abstractions (\ie ``games'') developed by
Kwiatkowska et al.\ as a foundation.
We define an abstraction preorder for these game abstractions which
enables us to identify many new game abstractions for each MDP ---
ranging from compact and imprecise to complex and precise.
This added ability to trade precision for efficiency
is crucial for scalable software model
checking, as precise abstractions are expensive to construct in
practice.
Furthermore, we develop a four-valued probabilistic computation tree
logic (PCTL) semantics for game abstractions.
Together, the preorder and PCTL semantics comprise a powerful verification and
refutation framework for arbitrary PCTL properties of MDPs.
Cite as
Mark Kattenbelt and Michael Huth. Verification and Refutation of Probabilistic Specifications via Games. In IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 4, pp. 251-262, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2009)
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@InProceedings{kattenbelt_et_al:LIPIcs.FSTTCS.2009.2323,
author = {Kattenbelt, Mark and Huth, Michael},
title = {{Verification and Refutation of Probabilistic Specifications via Games}},
booktitle = {IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science},
pages = {251--262},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-13-2},
ISSN = {1868-8969},
year = {2009},
volume = {4},
editor = {Kannan, Ravi and Narayan Kumar, K.},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2009.2323},
URN = {urn:nbn:de:0030-drops-23233},
doi = {10.4230/LIPIcs.FSTTCS.2009.2323},
annote = {Keywords: Probabilistic model checking, Markov decision processes, Abstraction preorder, Stochastic two-player games}
}
Document
Approximating Fault-Tolerant Group-Steiner Problems
Abstract
In this paper, we initiate the study of designing approximation algorithms for
{\sf Fault-Tolerant Group-Steiner} ({\sf FTGS}) problems. The motivation is to protect
the well-studied group-Steiner networks from edge or vertex failures.
In {\sf Fault-Tolerant Group-Steiner} problems, we are given a graph with edge- (or vertex-) costs,
a root vertex, and a collection of subsets of vertices called groups. The objective is to find a
minimum-cost subgraph that has two edge- (or vertex-) disjoint paths from each group to the root.
We present approximation algorithms and hardness results for several variants of this basic problem, e.g.,
edge-costs vs. vertex-costs, edge-connectivity vs. vertex-connectivity,
and $2$-connecting from each group a single vertex vs. many vertices.
Main contributions of our paper include the introduction
of very general structural lemmas on connectivity and a charging scheme that may find more applications in the future.
Our algorithmic results are supplemented by inapproximability results, which are tight in some cases.
Our algorithms employ a variety of techniques.
For the edge-connectivity variant, we use a primal-dual based
algorithm for covering an {\em uncros\-sable} set-family, while for the vertex-connectivity version,
we prove a new graph-theoretic lemma that shows equivalence between obtaining two vertex-disjoint paths
from two vertices and $2$-connecting a carefully chosen single vertex. To handle large group-sizes,
we use a $p$-Steiner tree algorithm to identify the ``correct'' pair of terminals from each group to be
connected to the root. We also use a non-trivial charging scheme
to improve the approximation ratio for the most general problem we consider.
Cite as
Rohit Khandekar, Guy Kortsarz, and Zeev Nutov. Approximating Fault-Tolerant Group-Steiner Problems. In IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 4, pp. 263-274, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2009)
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@InProceedings{khandekar_et_al:LIPIcs.FSTTCS.2009.2324,
author = {Khandekar, Rohit and Kortsarz, Guy and Nutov, Zeev},
title = {{Approximating Fault-Tolerant Group-Steiner Problems}},
booktitle = {IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science},
pages = {263--274},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-13-2},
ISSN = {1868-8969},
year = {2009},
volume = {4},
editor = {Kannan, Ravi and Narayan Kumar, K.},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2009.2324},
URN = {urn:nbn:de:0030-drops-23243},
doi = {10.4230/LIPIcs.FSTTCS.2009.2324},
annote = {Keywords: Fault-tolerance, group Steiner problem, edge-disjointness, vertex-disjointness, approximation, connectivity}
}
Document
Bounded Size Graph Clustering with Applications to Stream Processing
Abstract
We introduce a graph clustering problem motivated by a stream processing application. Input to our problem is an undirected graph with vertex and edge weights. A cluster is a subset of the vertices. The {\em size} of a cluster is
defined as the total vertex weight in the subset plus the total edge weight at the boundary of the cluster. The bounded size graph clustering problem ($\GC$) is to partition the vertices into clusters of size at most a given budget and minimize the total edge-weight across the clusters. In the {\em multiway cut} version of the problem, we are also given a subset of vertices called {\em terminals}. No cluster is allowed to contain more than one terminal. Our problem differs from most of the previously studied clustering problems in that the number of clusters is not specified. We first show that the feasibility version of the multiway cut $\GC$ problem,
i.e., determining if there exists a clustering with bounded-size clusters satisfying the multiway cut constraint, can be solved in polynomial time. Our algorithm is based on the min-cut subroutine and an uncrossing argument. This result is in contrast with the NP-hardness of the min-max multiway cut problem, considered by Svitkina and Tardos (2004), in which the number of clusters must equal the number of terminals. Our results for the feasibility version also generalize to any symmetric submodular function. We next show that the optimization version of $\GC$ is NP-hard by showing an
approximation-preserving reduction from the $\frac 13$-balanced cut problem.
Our main result is an $O(\log^2 n)$-approximation to the optimization version
of the multiway cut $\GC$ problem violating the budget by an $O(\log n)$
factor, where $n$ denotes the number of vertices. Our algorithm is based on a
set-cover-like greedy approach which iteratively computes bounded-size clusters
to maximize the number of new vertices covered.
Cite as
Rohit Khandekar, Kirsten Hildrum, Sujay Parekh, Deepak Rajan, Jay Sethuraman, and Joel Wolf. Bounded Size Graph Clustering with Applications to Stream Processing. In IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 4, pp. 275-286, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2009)
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@InProceedings{khandekar_et_al:LIPIcs.FSTTCS.2009.2325,
author = {Khandekar, Rohit and Hildrum, Kirsten and Parekh, Sujay and Rajan, Deepak and Sethuraman, Jay and Wolf, Joel},
title = {{Bounded Size Graph Clustering with Applications to Stream Processing}},
booktitle = {IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science},
pages = {275--286},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-13-2},
ISSN = {1868-8969},
year = {2009},
volume = {4},
editor = {Kannan, Ravi and Narayan Kumar, K.},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2009.2325},
URN = {urn:nbn:de:0030-drops-23250},
doi = {10.4230/LIPIcs.FSTTCS.2009.2325},
annote = {Keywords: Graph partitioning, uncrossing, Gomory-Hu trees, symmetric submodular functions}
}
Document
A Fine-grained Analysis of a Simple Independent Set Algorithm
Abstract
We present a simple exact algorithm for the \is\ problem with a runtime bounded
by $O(\rt^n \poly(n))$. This bound is obtained by, firstly, applying a new
branching rule and, secondly, by a distinct, computer-aided case analysis.
The new branching rule uses the concept of satellites and has previously only
been used in an algorithm for sparse graphs.
The computer-aided case analysis allows us to capture the behavior of our algorithm
in more detail than in a traditional analysis.
The main purpose of this paper is to demonstrate how a very simple
algorithm can outperform more complicated ones if the right analysis
of its running time is performed.
Cite as
Joachim Kneis, Alexander Langer, and Peter Rossmanith. A Fine-grained Analysis of a Simple Independent Set Algorithm. In IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 4, pp. 287-298, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2009)
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@InProceedings{kneis_et_al:LIPIcs.FSTTCS.2009.2326,
author = {Kneis, Joachim and Langer, Alexander and Rossmanith, Peter},
title = {{A Fine-grained Analysis of a Simple Independent Set Algorithm}},
booktitle = {IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science},
pages = {287--298},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-13-2},
ISSN = {1868-8969},
year = {2009},
volume = {4},
editor = {Kannan, Ravi and Narayan Kumar, K.},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2009.2326},
URN = {urn:nbn:de:0030-drops-23269},
doi = {10.4230/LIPIcs.FSTTCS.2009.2326},
annote = {Keywords: Exact Algorithms, Independent Set, Computer-aided Proof}
}
Document
Using Elimination Theory to construct Rigid Matrices
Abstract
The rigidity of a matrix $A$ for target rank $r$ is the minimum number
of entries of $A$ that must be changed to ensure that the rank of
the altered matrix is at most $r$. Since its introduction by Valiant
\cite{Val77}, rigidity and similar rank-robustness functions of
matrices have found numerous applications in circuit complexity,
communication complexity, and learning complexity. Almost all $\nbyn$
matrices over an infinite field have a rigidity of $(n-r)^2$. It is a
long-standing open question to construct infinite families of
\emph{explicit} matrices even with superlinear rigidity when $r=\Omega(n)$.
In this paper, we construct an infinite family of complex matrices
with the largest possible, i.e., $(n-r)^2$, rigidity. The entries of
an $\nbyn$ matrix in this family are distinct primitive roots of unity
of orders roughly \SL{$\exp(n^4 \log n)$}. To the best of our knowledge, this is
the first family of concrete (but not entirely explicit) matrices
having maximal rigidity and a succinct algebraic description.
Our construction is based on elimination theory of polynomial
ideals. In particular, we use results on the existence of polynomials
in elimination ideals with effective degree upper bounds (effective
Nullstellensatz). Using elementary algebraic geometry, we prove that
the dimension of the affine variety of matrices of rigidity at
most $k$ is exactly $n^2 - (n-r)^2 +k$. Finally, we use elimination theory to
examine whether the rigidity function is semicontinuous.
Cite as
Abhinav Kumar, Satyanarayana V. Lokam, Vijay M. Patankar, and Jayalal Sarma M. N.. Using Elimination Theory to construct Rigid Matrices. In IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 4, pp. 299-310, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2009)
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@InProceedings{kumar_et_al:LIPIcs.FSTTCS.2009.2327,
author = {Kumar, Abhinav and Lokam, Satyanarayana V. and Patankar, Vijay M. and Sarma M. N., Jayalal},
title = {{Using Elimination Theory to construct Rigid Matrices}},
booktitle = {IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science},
pages = {299--310},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-13-2},
ISSN = {1868-8969},
year = {2009},
volume = {4},
editor = {Kannan, Ravi and Narayan Kumar, K.},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2009.2327},
URN = {urn:nbn:de:0030-drops-23278},
doi = {10.4230/LIPIcs.FSTTCS.2009.2327},
annote = {Keywords: Matrix Rigidity, Lower Bounds, Circuit Complexity}
}
Document
On Nondeterministic Unranked Tree Automata with Sibling Constraints
Abstract
We continue the study of bottom-up unranked tree automata with equality and
disequality constraints between direct subtrees. In particular, we show that
the emptiness problem for the nondeterministic automata is decidable. In
addition, we show that the universality problem, in contrast, is undecidable.
Cite as
Christof Löding and Karianto Wong. On Nondeterministic Unranked Tree Automata with Sibling Constraints. In IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 4, pp. 311-322, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2009)
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@InProceedings{loding_et_al:LIPIcs.FSTTCS.2009.2328,
author = {L\"{o}ding, Christof and Wong, Karianto},
title = {{On Nondeterministic Unranked Tree Automata with Sibling Constraints}},
booktitle = {IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science},
pages = {311--322},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-13-2},
ISSN = {1868-8969},
year = {2009},
volume = {4},
editor = {Kannan, Ravi and Narayan Kumar, K.},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2009.2328},
URN = {urn:nbn:de:0030-drops-23281},
doi = {10.4230/LIPIcs.FSTTCS.2009.2328},
annote = {Keywords: Unranked tree automata, equality and disequality constraints, monadic second-order logic}
}
Document
Functionally Private Approximations of Negligibly-Biased Estimators
Abstract
We study functionally private approximations.
An approximation function $g$ is {\em functionally private} with respect to
$f$ if, for any input $x$, $g(x)$ reveals no more information about $x$ than
$f(x)$.
Our main result states that a function $f$ admits an efficiently-computable
functionally private approximation $g$ if there exists an efficiently-computable
and negligibly-biased estimator for $f$.
Contrary to previous generic results, our theorem is more general and
has a wider application reach.We provide two distinct applications of the above result to demonstrate its flexibility.
In the data stream model, we provide a functionally private approximation to the
$L_p$-norm estimation problem, a quintessential application in streaming, using only
polylogarithmic space in the input size.
The privacy guarantees rely on the use of pseudo-random {\em
functions} (PRF) (a stronger cryptographic notion than pseudo-random
generators) of which can be based on common cryptographic assumptions.The application of PRFs in this context appears to be novel and we expect other results to follow suit.Moreover, this is the first known functionally private streaming result for {\em any} problem.
Our second application result states that every problem in some subclasses of \SP of
hard counting problems admit efficient and functionally private approximation protocols.
This result is based on a functionally private approximation for the \SDNF
problem (or estimating the number of satisfiable truth assignments to a
Boolean formula in disjunctive normal form), which is an application of our
main theorem and previously known results.
Cite as
André Madeira and S. Muthukrishnan. Functionally Private Approximations of Negligibly-Biased Estimators. In IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 4, pp. 323-334, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2009)
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@InProceedings{madeira_et_al:LIPIcs.FSTTCS.2009.2329,
author = {Madeira, Andr\'{e} and Muthukrishnan, S.},
title = {{Functionally Private Approximations of Negligibly-Biased Estimators}},
booktitle = {IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science},
pages = {323--334},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-13-2},
ISSN = {1868-8969},
year = {2009},
volume = {4},
editor = {Kannan, Ravi and Narayan Kumar, K.},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2009.2329},
URN = {urn:nbn:de:0030-drops-23298},
doi = {10.4230/LIPIcs.FSTTCS.2009.2329},
annote = {Keywords: Functional privacy, privacy, data streams, #P-complete}
}
Document
Nash Equilibrium in Generalised Muller Games
Abstract
We suggest that extending Muller games with preference ordering for
players is a natural way to reason about unbounded duration games. In
this context, we look at the standard solution concept of Nash
equilibrium for non-zero sum games. We show that Nash equilibria
always exists for such generalised Muller games on finite graphs and
present a procedure to compute an equilibrium strategy profile. We
also give a procedure to compute a subgame perfect equilibrium when it
exists in such games.
Cite as
Soumya Paul and Sunil Simon. Nash Equilibrium in Generalised Muller Games. In IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 4, pp. 335-346, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2009)
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@InProceedings{paul_et_al:LIPIcs.FSTTCS.2009.2330,
author = {Paul, Soumya and Simon, Sunil},
title = {{Nash Equilibrium in Generalised Muller Games}},
booktitle = {IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science},
pages = {335--346},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-13-2},
ISSN = {1868-8969},
year = {2009},
volume = {4},
editor = {Kannan, Ravi and Narayan Kumar, K.},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2009.2330},
URN = {urn:nbn:de:0030-drops-23304},
doi = {10.4230/LIPIcs.FSTTCS.2009.2330},
annote = {Keywords: Infinite games on graphs, Muller games, Nash equilibrium, subgame perfect equilibrium}
}
Document
Modelchecking counting properties of 1-safe nets with buffers in paraPSPACE
Abstract
We consider concurrent systems that can be modelled as $1$-safe
Petri nets communicating through a fixed set of buffers (modelled as
unbounded places). We identify a parameter $\ben$, which we call
``benefit depth'', formed from the communication graph between the
buffers. We show that for our system model, the coverability and boundedness
problems can be solved in polynomial space assuming $\ben$ to be a
fixed parameter, that is, the space requirement is $f(\ben)p(n)$,
where $f$ is an exponential function and $p$ is a polynomial in
the size of the input. We then obtain similar complexity bounds for
modelchecking a logic based on such counting properties.
This means that systems that have sparse communication patterns can
be analyzed more efficiently than using previously
known algorithms for general Petri nets.
Cite as
M. Praveen and Kamal Lodaya. Modelchecking counting properties of 1-safe nets with buffers in paraPSPACE. In IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 4, pp. 347-358, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2009)
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@InProceedings{praveen_et_al:LIPIcs.FSTTCS.2009.2331,
author = {Praveen, M. and Lodaya, Kamal},
title = {{Modelchecking counting properties of 1-safe nets with buffers in paraPSPACE}},
booktitle = {IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science},
pages = {347--358},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-13-2},
ISSN = {1868-8969},
year = {2009},
volume = {4},
editor = {Kannan, Ravi and Narayan Kumar, K.},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2009.2331},
URN = {urn:nbn:de:0030-drops-23314},
doi = {10.4230/LIPIcs.FSTTCS.2009.2331},
annote = {Keywords: Petri nets, Coverability, Boundedness, paraPSPACE}
}
Document
Synthesis of Finite-state and Definable Winning Strategies
Abstract
Church's Problem asks for the construction of a procedure which,
given a logical specification $\varphi$ on sequence pairs, realizes
for any input sequence $I$ an output sequence $O$ such that $(I,O)$
satisfies $\varphi$. McNaughton reduced Church's Problem to a problem about two-player$\omega$-games.
B\"uchi and Landweber gave a solution for
Monadic Second-Order Logic of Order ($\MLO$) specifications in terms of finite-state strategies.
We consider two natural generalizations of the Church problem to
countable ordinals: the first deals with finite-state strategies;
the second deals with $\MLO$-definable strategies. We investigate
games of arbitrary countable length and prove the computability of
these generalizations of Church's problem.
Cite as
Alexander Rabinovich. Synthesis of Finite-state and Definable Winning Strategies. In IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 4, pp. 359-370, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2009)
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@InProceedings{rabinovich:LIPIcs.FSTTCS.2009.2332,
author = {Rabinovich, Alexander},
title = {{Synthesis of Finite-state and Definable Winning Strategies}},
booktitle = {IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science},
pages = {359--370},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-13-2},
ISSN = {1868-8969},
year = {2009},
volume = {4},
editor = {Kannan, Ravi and Narayan Kumar, K.},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2009.2332},
URN = {urn:nbn:de:0030-drops-23320},
doi = {10.4230/LIPIcs.FSTTCS.2009.2332},
annote = {Keywords: Games of ordinal length, Church Synthesis Problem, Monadic Logic, Composition Method}
}
Document
The Power of Depth 2 Circuits over Algebras
Abstract
We study the problem of polynomial identity testing (PIT) for depth
$2$ arithmetic circuits over matrix algebra. We show that identity
testing of depth $3$ ($\Sigma \Pi \Sigma$) arithmetic circuits over a
field $\F$ is polynomial time equivalent to identity testing of depth
$2$ ($\Pi \Sigma$) arithmetic circuits over
$\mathsf{U}_2(\mathbb{F})$, the algebra of upper-triangular $2\times
2$ matrices with entries from $\F$. Such a connection is a bit
surprising since we also show that, as computational models, $\Pi
\Sigma$ circuits over $\mathsf{U}_2(\mathbb{F})$ are strictly `weaker'
than $\Sigma \Pi \Sigma$ circuits over $\mathbb{F}$. The equivalence
further implies that PIT of $\Sigma \Pi \Sigma$ circuits reduces to PIT
of width-$2$ commutative \emph{Algebraic Branching
Programs}(ABP). Further, we give a deterministic polynomial time
identity testing algorithm for a $\Pi \Sigma$ circuit of size $s$ over
commutative algebras of dimension $O(\log s/\log\log s)$ over
$\F$. Over commutative algebras of dimension $\poly(s)$, we show that
identity testing of $\Pi \Sigma$ circuits is at least as hard as that
of $\Sigma \Pi \Sigma$ circuits over $\mathbb{F}$.
Cite as
Chandan Saha, Ramprasad Saptharishi, and Nitin Saxena. The Power of Depth 2 Circuits over Algebras. In IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 4, pp. 371-382, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2009)
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@InProceedings{saha_et_al:LIPIcs.FSTTCS.2009.2333,
author = {Saha, Chandan and Saptharishi, Ramprasad and Saxena, Nitin},
title = {{The Power of Depth 2 Circuits over Algebras}},
booktitle = {IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science},
pages = {371--382},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-13-2},
ISSN = {1868-8969},
year = {2009},
volume = {4},
editor = {Kannan, Ravi and Narayan Kumar, K.},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2009.2333},
URN = {urn:nbn:de:0030-drops-23334},
doi = {10.4230/LIPIcs.FSTTCS.2009.2333},
annote = {Keywords: Polynomial identity testing, depth 3 circuits, matrix algebras, local rings}
}
Document
Deductive Verification of Continuous Dynamical Systems
Abstract
We define the notion of inductive invariants for
continuous dynamical systems and use it
to present inference rules for
safety verification of polynomial continuous
dynamical systems.
We present two different sound and complete inference
rules, but neither of these rules can be effectively applied.
We then present several simpler and practical
inference rules that are sound and relatively complete
for different classes of inductive invariants.
The simpler inference rules can be effectively checked when
all involved sets are semi-algebraic.
Cite as
Ankur Taly and Ashish Tiwari. Deductive Verification of Continuous Dynamical Systems. In IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 4, pp. 383-394, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2009)
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@InProceedings{taly_et_al:LIPIcs.FSTTCS.2009.2334,
author = {Taly, Ankur and Tiwari, Ashish},
title = {{Deductive Verification of Continuous Dynamical Systems}},
booktitle = {IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science},
pages = {383--394},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-13-2},
ISSN = {1868-8969},
year = {2009},
volume = {4},
editor = {Kannan, Ravi and Narayan Kumar, K.},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2009.2334},
URN = {urn:nbn:de:0030-drops-23342},
doi = {10.4230/LIPIcs.FSTTCS.2009.2334},
annote = {Keywords: Deductive Verification, inductive invariants, continuous and hybrid dynamical systems, Theory of Reals}
}
Document
Recurrence and Transience for Probabilistic Automata
Abstract
In a context of $\omega$-regular specifications for infinite execution
sequences, the classical B\"uchi condition, or repeated liveness
condition, asks that an accepting state is visited infinitely often. In
this paper, we show that in a probabilistic context it is relevant to
strengthen this infinitely often condition. An execution path is now
accepting if the \emph{proportion} of time spent on an accepting state
does not go to zero as the length of the path goes to infinity. We
introduce associated notions of recurrence and transience for
non-homogeneous finite Markov chains and study the computational
complexity of the associated problems. As Probabilistic B\"uchi Automata
(PBA) have been an attempt to generalize B\"uchi automata to a
probabilistic context, we define a class of Constrained Probabilistic
Automata with our new accepting condition on runs. The accepted language
is defined by the requirement that the measure of the set of accepting
runs is positive (probable semantics) or equals 1 (almost-sure
semantics). In contrast to the PBA case, we prove that
the emptiness problem for the language of a constrained probabilistic
B\"uchi automaton with the probable semantics is decidable.
Cite as
Mathieu Tracol, Christel Baier, and Marcus Grösser. Recurrence and Transience for Probabilistic Automata. In IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 4, pp. 395-406, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2009)
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@InProceedings{tracol_et_al:LIPIcs.FSTTCS.2009.2335,
author = {Tracol, Mathieu and Baier, Christel and Gr\"{o}sser, Marcus},
title = {{Recurrence and Transience for Probabilistic Automata}},
booktitle = {IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science},
pages = {395--406},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-13-2},
ISSN = {1868-8969},
year = {2009},
volume = {4},
editor = {Kannan, Ravi and Narayan Kumar, K.},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2009.2335},
URN = {urn:nbn:de:0030-drops-23357},
doi = {10.4230/LIPIcs.FSTTCS.2009.2335},
annote = {Keywords: Markov Chains, Probabilistic Automata, Buchi Automata, Recurrence, Omega-Regular Properties}
}
Document
Structure and Specification as Sources of Complexity
Abstract
If computational complexity is the study of what makes certain computational
problems inherently difficult to solve, an important contribution of
descriptive complexity in this regard is the separation it provides between
the specification of a decision problem and the structure against which this
specification is checked. The formalisation of these two aspects leads to
tools for studying them as sources of complexity, and on the one hand leads to
results in the characterisation of complexity classes and on the other elates
to parameterized complexity. In these notes accompanying the invited talk,
some definitions and results are presented leading to recent work on the
characterisation of polynomial time and on the parameterized complexity of
first-order logic on restricted graph classes.
Cite as
Anuj Dawar. Structure and Specification as Sources of Complexity. In IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 4, pp. 407-416, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2009)
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@InProceedings{dawar:LIPIcs.FSTTCS.2009.2336,
author = {Dawar, Anuj},
title = {{Structure and Specification as Sources of Complexity}},
booktitle = {IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science},
pages = {407--416},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-13-2},
ISSN = {1868-8969},
year = {2009},
volume = {4},
editor = {Kannan, Ravi and Narayan Kumar, K.},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2009.2336},
URN = {urn:nbn:de:0030-drops-23365},
doi = {10.4230/LIPIcs.FSTTCS.2009.2336},
annote = {Keywords: Computational Complexity, Descriptive Complexity, Logical Complexity, Parametrized Complexity, Locality, Automata}
}
Document
Priced Timed Automata: Theory and Tools
Abstract
Priced timed automata are emerging as useful formalisms for modeling
and analysing a broad range of resource allocation problems. In
this extended abstract, we highlight recent (un)deci\-dability results
related to priced timed automata as well as point to a number of
open problems.
Cite as
Kim G. Larsen. Priced Timed Automata: Theory and Tools. In IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 4, pp. 417-425, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2009)
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@InProceedings{larsen:LIPIcs.FSTTCS.2009.2337,
author = {Larsen, Kim G.},
title = {{Priced Timed Automata: Theory and Tools}},
booktitle = {IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science},
pages = {417--425},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-13-2},
ISSN = {1868-8969},
year = {2009},
volume = {4},
editor = {Kannan, Ravi and Narayan Kumar, K.},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2009.2337},
URN = {urn:nbn:de:0030-drops-23374},
doi = {10.4230/LIPIcs.FSTTCS.2009.2337},
annote = {Keywords: Timed systems, optimal scheduling, priced timed automata, games, model-checking}
}
Document
Fighting bit Rot with Types (Experience Report: Scala Collections)
Abstract
We report on our experiences in redesigning Scala's collection
libraries, focussing on the role that type systems play in keeping
software architectures coherent over time. Type systems can make
software architecture more explicit but, if they are too weak, can
also cause code duplication. We show that code duplication can be
avoided using two of Scala's type constructions: higher-kinded types
and implicit parameters and conversions.
Cite as
Martin Odersky and Adriaan Moors. Fighting bit Rot with Types (Experience Report: Scala Collections). In IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 4, pp. 427-451, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2009)
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@InProceedings{odersky_et_al:LIPIcs.FSTTCS.2009.2338,
author = {Odersky, Martin and Moors, Adriaan},
title = {{Fighting bit Rot with Types (Experience Report: Scala Collections)}},
booktitle = {IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science},
pages = {427--451},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-13-2},
ISSN = {1868-8969},
year = {2009},
volume = {4},
editor = {Kannan, Ravi and Narayan Kumar, K.},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2009.2338},
URN = {urn:nbn:de:0030-drops-23386},
doi = {10.4230/LIPIcs.FSTTCS.2009.2338},
annote = {Keywords: Programming languages, scala, avoiding code duplication, higher-order kinds, type systems, polymorphism, collections library}
}
Document
Iterative Methods in Combinatorial Optimization
Abstract
We describe a simple iterative method for proving a variety of results in combinatorial optimization. It is inspired by Jain's iterative rounding method (FOCS 1998) for designing approximation algorithms for survivable network design problems, and augmented with a relaxation idea in the work of Lau, Naor, Salvatipour and Singh (STOC 2007) on designing an approximation algorithm for its degree bounded version. At the heart of the method is a counting argument that redistributes tokens from the columns to the rows of an LP extreme point. This token argument was further refined to
fractional assignment and redistribution in work of Bansal, Khandekar and Nagarajan on degree-bounded directed network design (STOC 2008). In this presentation, we introduce the method using the assignment problem, describe its application to showing the integrality of Edmond's characterization (1971) of the spanning tree polyhedron, and then extend the argument to show a simple proof of the Singh and Lau's approximation
algorithm (STOC 2007) for its degree constrained version, due to Bansal, Khandekar and Nagarajan. We conclude by showing how Jain's original proof can also be simplified by using a fractional token argument (joint work with
Nagarajan and Singh).
This presentation is extracted from an upcoming monograph on this topic
co-authored with Lau and Singh.
Cite as
R. Ravi. Iterative Methods in Combinatorial Optimization. In IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 4, pp. 453-469, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2009)
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@InProceedings{ravi:LIPIcs.FSTTCS.2009.2339,
author = {Ravi, R.},
title = {{Iterative Methods in Combinatorial Optimization}},
booktitle = {IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science},
pages = {453--469},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-13-2},
ISSN = {1868-8969},
year = {2009},
volume = {4},
editor = {Kannan, Ravi and Narayan Kumar, K.},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2009.2339},
URN = {urn:nbn:de:0030-drops-23391},
doi = {10.4230/LIPIcs.FSTTCS.2009.2339},
annote = {Keywords: Iterative methods, combinatorial optimization, network design, approximation algorithms, assignment problem, linear programming}
}
Document
Randomness extractors -- applications and constructions
Abstract
Randomness extractors are efficient algorithms which convert weak random sources into nearly perfect ones. While such purification of randomness was the original motivation for constructing extractors, these constructions turn out to have strong pseudorandom properties which found applications in diverse areas of computer science and combinatorics. We will highlight some of the
applications, as well as recent constructions achieving near-optimal
extraction.
Cite as
Avi Wigderson. Randomness extractors -- applications and constructions. In IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 4, pp. 471-473, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2009)
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@InProceedings{wigderson:LIPIcs.FSTTCS.2009.2340,
author = {Wigderson, Avi},
title = {{Randomness extractors -- applications and constructions}},
booktitle = {IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science},
pages = {471--473},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-939897-13-2},
ISSN = {1868-8969},
year = {2009},
volume = {4},
editor = {Kannan, Ravi and Narayan Kumar, K.},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2009.2340},
URN = {urn:nbn:de:0030-drops-23407},
doi = {10.4230/LIPIcs.FSTTCS.2009.2340},
annote = {Keywords: Randomness extractors, weak random sources, purification of randomness}
}