40 Search Results for "Vinay, V"


Volume

LIPIcs, Volume 2

IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science

FSTTCS 2008, December 9-11, 2008, Bangalore, India

Editors: Ramesh Hariharan, Madhavan Mukund, and V Vinay

Document
Determinants vs. Algebraic Branching Programs

Authors: Abhranil Chatterjee, Mrinal Kumar, and Ben Lee Volk

Published in: LIPIcs, Volume 287, 15th Innovations in Theoretical Computer Science Conference (ITCS 2024)


Abstract
We show that for every homogeneous polynomial of degree d, if it has determinantal complexity at most s, then it can be computed by a homogeneous algebraic branching program (ABP) of size at most O(d⁵s). Moreover, we show that for most homogeneous polynomials, the width of the resulting homogeneous ABP is just s-1 and the size is at most O(ds). Thus, for constant degree homogeneous polynomials, their determinantal complexity and ABP complexity are within a constant factor of each other and hence, a super-linear lower bound for ABPs for any constant degree polynomial implies a super-linear lower bound on determinantal complexity; this relates two open problems of great interest in algebraic complexity. As of now, super-linear lower bounds for ABPs are known only for polynomials of growing degree [Mrinal Kumar, 2019; Prerona Chatterjee et al., 2022], and for determinantal complexity the best lower bounds are larger than the number of variables only by a constant factor [Mrinal Kumar and Ben Lee Volk, 2022]. While determinantal complexity and ABP complexity are classically known to be polynomially equivalent [Meena Mahajan and V. Vinay, 1997], the standard transformation from the former to the latter incurs a polynomial blow up in size in the process, and thus, it was unclear if a super-linear lower bound for ABPs implies a super-linear lower bound on determinantal complexity. In particular, a size preserving transformation from determinantal complexity to ABPs does not appear to have been known prior to this work, even for constant degree polynomials.

Cite as

Abhranil Chatterjee, Mrinal Kumar, and Ben Lee Volk. Determinants vs. Algebraic Branching Programs. In 15th Innovations in Theoretical Computer Science Conference (ITCS 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 287, pp. 27:1-27:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)


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@InProceedings{chatterjee_et_al:LIPIcs.ITCS.2024.27,
  author =	{Chatterjee, Abhranil and Kumar, Mrinal and Volk, Ben Lee},
  title =	{{Determinants vs. Algebraic Branching Programs}},
  booktitle =	{15th Innovations in Theoretical Computer Science Conference (ITCS 2024)},
  pages =	{27:1--27:13},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-309-6},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{287},
  editor =	{Guruswami, Venkatesan},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITCS.2024.27},
  URN =		{urn:nbn:de:0030-drops-195550},
  doi =		{10.4230/LIPIcs.ITCS.2024.27},
  annote =	{Keywords: Determinant, Algebraic Branching Program, Lower Bounds, Singular Variety}
}
Document
Complete Volume
LIPIcs, Volume 2, FSTTCS'08, Complete Volume

Authors: Ramesh Hariharan, Madhavan Mukund, and V Vinay

Published in: LIPIcs, Volume 2, IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (2008)


Abstract
LIPIcs, Volume 2, FSTTCS'08, Complete Volume

Cite as

IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 2, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2013)


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@Proceedings{hariharan_et_al:LIPIcs.FSTTCS.2008,
  title =	{{LIPIcs, Volume 2, FSTTCS'08, Complete Volume}},
  booktitle =	{IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-08-8},
  ISSN =	{1868-8969},
  year =	{2013},
  volume =	{2},
  editor =	{Hariharan, Ramesh and Mukund, Madhavan and Vinay, V},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2008},
  URN =		{urn:nbn:de:0030-drops-40966},
  doi =		{10.4230/LIPIcs.FSTTCS.2008},
  annote =	{Keywords: LIPIcs, Volume 2, FSTTCS'08, Complete Volume}
}
Document
Front Matter
2008 Abstracts Collection -- IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science

Authors: Ramesh Hariharan, Madhavan Mukund, and V Vinay

Published in: LIPIcs, Volume 2, IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (2008)


Abstract
This volume contains the proceedings of the 28th international conference on the Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2008), organized under the auspices of the Indian Association for Research in Computing Science (IARCS).

Cite as

IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 2, pp. i-xviii, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2008)


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@InProceedings{hariharan_et_al:LIPIcs.FSTTCS.2008.1772,
  author =	{Hariharan, Ramesh and Mukund, Madhavan and Vinay, V},
  title =	{{2008 Abstracts Collection -- IARCS Annual Conference on  Foundations of Software Technology and Theoretical Computer Science}},
  booktitle =	{IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science},
  pages =	{i--xviii},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-08-8},
  ISSN =	{1868-8969},
  year =	{2008},
  volume =	{2},
  editor =	{Hariharan, Ramesh and Mukund, Madhavan and Vinay, V},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2008.1772},
  URN =		{urn:nbn:de:0030-drops-17720},
  doi =		{10.4230/LIPIcs.FSTTCS.2008.1772},
  annote =	{Keywords: }
}
Document
2008 Preface -- IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science

Authors: Ramesh Hariharan, Madhavan Mukund, and V Vinay

Published in: LIPIcs, Volume 2, IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (2008)


Abstract
This volume contains the proceedings of the 28th international conference on the Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2008), organized under the auspices of the Indian Association for Research in Computing Science (IARCS). This year's conference attracted 117 submissions. Each submission was reviewed by at least three independent referees. The final selection of the papers making up the programme was done through an electronic discussion on EasyChair, spanning two weeks, without a physical meeting of the Programme Committee (PC). All PC members participated actively in the discussion. We have five invited speakers this year: Hubert Comon-Lundh, Uriel Feige, Erich Graedel, Simon Peyton Jones and Leslie Valiant. We thank them for having readily accepted our invitation to talk at the conference and for providing abstracts (and even full papers) for the proceedings. We thank all the reviewers and PC members, without whose dedicated effort the conference would not be possible. We thank the Organizing Committee for making the arrangements for the conference. This year, the conference is being held at the Indian Institute of Science, Bangalore, as part of its centenary year celebrations. It is a great honour and privilege for the conference to be recognized and associated with the institute on this occasion. Finally, this year we have taken a decisive step in democratizing the conference by moving away from commercial publishers. Instead, we will be hosting the proceedings online, electronically, via the Dagstuhl Research Online Publication Server (DROPS). A complete copy of the proceedings will also be hosted on the FSTTCS website (www.fsttcs.org). The copyrights to the papers will reside not with the publishers but with the respective authors. The copyright is now governed by the Creative Commons attribution NC-ND. We do hope this direction will be sustained in the future.

Cite as

Ramesh Hariharan, Madhavan Mukund, and V Vinay. 2008 Preface -- IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science. In IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 2, p. -1, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2008)


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@InProceedings{hariharan_et_al:LIPIcs.FSTTCS.2008.1771,
  author =	{Hariharan, Ramesh and Mukund, Madhavan and Vinay, V},
  title =	{{2008 Preface -- IARCS Annual Conference on  Foundations of Software Technology and Theoretical Computer Science}},
  booktitle =	{IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science},
  pages =	{-1---1},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-08-8},
  ISSN =	{1868-8969},
  year =	{2008},
  volume =	{2},
  editor =	{Hariharan, Ramesh and Mukund, Madhavan and Vinay, V},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2008.1771},
  URN =		{urn:nbn:de:0030-drops-17713},
  doi =		{10.4230/LIPIcs.FSTTCS.2008.1771},
  annote =	{Keywords: Preface}
}
Document
3-connected Planar Graph Isomorphism is in Log-space

Authors: Samir Datta, Nutan Limaye, and Prajakta Nimbhorkar

Published in: LIPIcs, Volume 2, IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (2008)


Abstract
We consider the isomorphism and canonization problem for $3$-connected planar graphs. The problem was known to be \Log-hard and in \ULcoUL\ \cite{TW07}. In this paper, we give a deterministic log-space algorithm for $3$-connected planar graph isomorphism and canonization. This gives an \Log-completeness result, thereby settling its complexity. \par The algorithm uses the notion of universal exploration sequences from \cite{koucky01} and \cite{Rei05}. To our knowledge, this is a completely new approach to graph canonization.

Cite as

Samir Datta, Nutan Limaye, and Prajakta Nimbhorkar. 3-connected Planar Graph Isomorphism is in Log-space. In IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 2, pp. 155-162, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2008)


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@InProceedings{datta_et_al:LIPIcs.FSTTCS.2008.1749,
  author =	{Datta, Samir and Limaye, Nutan and Nimbhorkar, Prajakta},
  title =	{{3-connected Planar Graph Isomorphism is in Log-space}},
  booktitle =	{IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science},
  pages =	{155--162},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-08-8},
  ISSN =	{1868-8969},
  year =	{2008},
  volume =	{2},
  editor =	{Hariharan, Ramesh and Mukund, Madhavan and Vinay, V},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2008.1749},
  URN =		{urn:nbn:de:0030-drops-17491},
  doi =		{10.4230/LIPIcs.FSTTCS.2008.1749},
  annote =	{Keywords: Planar graph isomorphism, three connected graphs, logspace, universal exploration sequence}
}
Document
A Cubic-Vertex Kernel for Flip Consensus Tree

Authors: Christian Komusiewicz and Johannes Uhlmann

Published in: LIPIcs, Volume 2, IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (2008)


Abstract
Given a bipartite graph G=(V_c,V_t,E) and a non-negative integer k, the NP-complete Minimum-Flip Consensus Tree problem asks whether G can be transformed, using up to k edge insertions and deletions, into a graph that does not contain an induced P_5 with its first vertex in V_t (a so-called M-graph or Sigma-graph). This problem plays an important role in computational phylogenetics, V_c standing for the characters and V_t standing for taxa. Chen et al. [IEEE/ACM TCBB 2006] showed that Minimum-Flip Consensus Tree is NP-complete and presented a parameterized algorithm with running time O(6^k\cdot |V_t|\cdot |V_c|). Recently, Boecker et al. [IWPEC'08] presented a refined search tree algorithm with running time O(4.83^k(|V_t|+|V_c|) + |V_t|\cdot |V_c|). We complement these results by polynomial-time executable data reduction rules yielding a problem kernel with O(k^3) vertices.

Cite as

Christian Komusiewicz and Johannes Uhlmann. A Cubic-Vertex Kernel for Flip Consensus Tree. In IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 2, pp. 280-291, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2008)


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@InProceedings{komusiewicz_et_al:LIPIcs.FSTTCS.2008.1760,
  author =	{Komusiewicz, Christian and Uhlmann, Johannes},
  title =	{{A Cubic-Vertex Kernel for Flip Consensus Tree}},
  booktitle =	{IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science},
  pages =	{280--291},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-08-8},
  ISSN =	{1868-8969},
  year =	{2008},
  volume =	{2},
  editor =	{Hariharan, Ramesh and Mukund, Madhavan and Vinay, V},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2008.1760},
  URN =		{urn:nbn:de:0030-drops-17600},
  doi =		{10.4230/LIPIcs.FSTTCS.2008.1760},
  annote =	{Keywords: Fixed-parameter algorithm, problem kernel, NP-hard problem, graph modification problem, computational phylogenetics}
}
Document
A Hierarchy of Semantics for Non-deterministic Term Rewriting Systems

Authors: Juan Rodriguez-Hortala

Published in: LIPIcs, Volume 2, IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (2008)


Abstract
Formalisms involving some degree of nondeterminism are frequent in computer science. In particular, various programming or specification languages are based on term rewriting systems where confluence is not required. In this paper we examine three concrete possible semantics for non-determinism that can be assigned to those programs. Two of them --call-time choice and run-time choice-- are quite well-known, while the third one --plural semantics-- is investigated for the first time in the context of term rewriting based programming languages. We investigate some basic intrinsic properties of the semantics and establish some relationships between them: we show that the three semantics form a hierarchy in the sense of set inclusion, and we prove that call-time choice and plural semantics enjoy a remarkable compositionality property that fails for run-time choice; finally, we show how to express plural semantics within run-time choice by means of a program transformation, for which we prove its adequacy.

Cite as

Juan Rodriguez-Hortala. A Hierarchy of Semantics for Non-deterministic Term Rewriting Systems. In IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 2, pp. 328-339, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2008)


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@InProceedings{rodriguezhortala:LIPIcs.FSTTCS.2008.1764,
  author =	{Rodriguez-Hortala, Juan},
  title =	{{A Hierarchy of Semantics for Non-deterministic Term Rewriting Systems}},
  booktitle =	{IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science},
  pages =	{328--339},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-08-8},
  ISSN =	{1868-8969},
  year =	{2008},
  volume =	{2},
  editor =	{Hariharan, Ramesh and Mukund, Madhavan and Vinay, V},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2008.1764},
  URN =		{urn:nbn:de:0030-drops-17643},
  doi =		{10.4230/LIPIcs.FSTTCS.2008.1764},
  annote =	{Keywords: Functional-logic programming, term rewriting systems, constructor-based rewriting logic, non-determinism, call-time choice semantics, run-time choice}
}
Document
A new approach to the planted clique problem

Authors: Alan Frieze and Ravi Kannan

Published in: LIPIcs, Volume 2, IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (2008)


Abstract
We study the problem of finding a large planted clique in the random graph $G_{n,1/2}$. We reduce the problem to that of maximising a three dimensional tensor over the unit ball in $n$ dimensions. This latter problem has not been well studied and so we hope that this reduction will eventually lead to an improved solution to the planted clique problem.

Cite as

Alan Frieze and Ravi Kannan. A new approach to the planted clique problem. In IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 2, pp. 187-198, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2008)


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@InProceedings{frieze_et_al:LIPIcs.FSTTCS.2008.1752,
  author =	{Frieze, Alan and Kannan, Ravi},
  title =	{{A new approach to the planted clique problem}},
  booktitle =	{IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science},
  pages =	{187--198},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-08-8},
  ISSN =	{1868-8969},
  year =	{2008},
  volume =	{2},
  editor =	{Hariharan, Ramesh and Mukund, Madhavan and Vinay, V},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2008.1752},
  URN =		{urn:nbn:de:0030-drops-17521},
  doi =		{10.4230/LIPIcs.FSTTCS.2008.1752},
  annote =	{Keywords: Planted Clique, Tensor, Random Graph}
}
Document
A new upper bound for 3-SAT

Authors: Josep Diaz, Lefteris Kirousis, Dieter Mitsche, and Xavier Perez-Gimenez

Published in: LIPIcs, Volume 2, IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (2008)


Abstract
We show that a randomly chosen $3$-CNF formula over $n$ variables with clauses-to-variables ratio at least $4.4898$ is asymptotically almost surely unsatisfiable. The previous best such bound, due to Dubois in 1999, was $4.506$. The first such bound, independently discovered by many groups of researchers since 1983, was $5.19$. Several decreasing values between $5.19$ and $4.506$ were published in the years between. The probabilistic techniques we use for the proof are, we believe, of independent interest.

Cite as

Josep Diaz, Lefteris Kirousis, Dieter Mitsche, and Xavier Perez-Gimenez. A new upper bound for 3-SAT. In IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 2, pp. 163-174, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2008)


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@InProceedings{diaz_et_al:LIPIcs.FSTTCS.2008.1750,
  author =	{Diaz, Josep and Kirousis, Lefteris and Mitsche, Dieter and Perez-Gimenez, Xavier},
  title =	{{A new upper bound for 3-SAT}},
  booktitle =	{IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science},
  pages =	{163--174},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-08-8},
  ISSN =	{1868-8969},
  year =	{2008},
  volume =	{2},
  editor =	{Hariharan, Ramesh and Mukund, Madhavan and Vinay, V},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2008.1750},
  URN =		{urn:nbn:de:0030-drops-17507},
  doi =		{10.4230/LIPIcs.FSTTCS.2008.1750},
  annote =	{Keywords: Satisfiability, 3-SAT, random, threshold}
}
Document
About models of security protocols

Authors: Hubert Comon-Lundh

Published in: LIPIcs, Volume 2, IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (2008)


Abstract
In this paper, mostly consisting of definitions, we revisit the models of security protocols: we show that the symbolic and the computational models (as well as others) are instances of a same generic model. Our definitions are also parametrized by the security primitives, the notion of attacker and, to some extent, the process calculus.

Cite as

Hubert Comon-Lundh. About models of security protocols. In IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 2, pp. 352-356, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2008)


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@InProceedings{comonlundh:LIPIcs.FSTTCS.2008.1766,
  author =	{Comon-Lundh, Hubert},
  title =	{{About  models of security protocols}},
  booktitle =	{IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science},
  pages =	{352--356},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-08-8},
  ISSN =	{1868-8969},
  year =	{2008},
  volume =	{2},
  editor =	{Hariharan, Ramesh and Mukund, Madhavan and Vinay, V},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2008.1766},
  URN =		{urn:nbn:de:0030-drops-17662},
  doi =		{10.4230/LIPIcs.FSTTCS.2008.1766},
  annote =	{Keywords: Protocols, security, concurrency, formal methods}
}
Document
Abstraction Refinement for Games with Incomplete Information

Authors: Rayna Dimitrova and Bernd Finkbeiner

Published in: LIPIcs, Volume 2, IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (2008)


Abstract
Counterexample-guided abstraction refinement (CEGAR) is used in automated software analysis to find suitable finite-state abstractions of infinite-state systems. In this paper, we extend CEGAR to games with incomplete information, as they commonly occur in controller synthesis and modular verification. The challenge is that, under incomplete information, one must carefully account for the knowledge available to the player: the strategy must not depend on information the player cannot see. We propose an abstraction mechanism for games under incomplete information that incorporates the approximation of the players\' moves into a knowledge-based subset construction on the abstract state space. This abstraction results in a perfect-information game over a finite graph. The concretizability of abstract strategies can be encoded as the satisfiability of strategy-tree formulas. Based on this encoding, we present an interpolation-based approach for selecting new predicates and provide sufficient conditions for the termination of the resulting refinement loop.

Cite as

Rayna Dimitrova and Bernd Finkbeiner. Abstraction Refinement for Games with Incomplete Information. In IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 2, pp. 175-186, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2008)


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@InProceedings{dimitrova_et_al:LIPIcs.FSTTCS.2008.1751,
  author =	{Dimitrova, Rayna and Finkbeiner, Bernd},
  title =	{{Abstraction Refinement for Games with Incomplete Information}},
  booktitle =	{IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science},
  pages =	{175--186},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-08-8},
  ISSN =	{1868-8969},
  year =	{2008},
  volume =	{2},
  editor =	{Hariharan, Ramesh and Mukund, Madhavan and Vinay, V},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2008.1751},
  URN =		{urn:nbn:de:0030-drops-17510},
  doi =		{10.4230/LIPIcs.FSTTCS.2008.1751},
  annote =	{Keywords: Automatic abstraction refinement, synthesis}
}
Document
Algorithms for Game Metrics

Authors: Krishnendu Chatterjee, Luca de Alfaro, Rupak Majumdar, and Vishwanath Raman

Published in: LIPIcs, Volume 2, IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (2008)


Abstract
Simulation and bisimulation metrics for stochastic systems provide a quantitative generalization of the classical simulation and bisimulation relations. These metrics capture the similarity of states with respect to quantitative specifications written in the quantitative $\mu$-calculus and related probabilistic logics. We present algorithms for computing the metrics on Markov decision processes (MDPs), turn-based stochastic games, and concurrent games. For turn-based games and MDPs, we provide a polynomial-time algorithm based on linear programming for the computation of the one-step metric distance between states. The algorithm improves on the previously known exponential-time algorithm based on a reduction to the theory of reals. We then present PSPACE algorithms for both the decision problem and the problem of approximating the metric distance between two states, matching the best known bound for Markov chains. For the bisimulation kernel of the metric, which corresponds to probabilistic bisimulation, our algorithm works in time $\calo(n^4)$ for both turn-based games and MDPs; improving the previously best known $\calo(n^9\cdot\log(n))$ time algorithm for MDPs. For a concurrent game $G$, we show that computing the exact distance between states is at least as hard as computing the value of concurrent reachability games and the square-root-sum problem in computational geometry. We show that checking whether the metric distance is bounded by a rational $r$, can be accomplished via a reduction to the theory of real closed fields, involving a formula with three quantifier alternations, yielding $\calo(|G|^{\calo(|G|^5)})$ time complexity, improving the previously known reduction with $\calo(|G|^{\calo(|G|^7)})$ time complexity. These algorithms can be iterated to approximate the metrics using binary search.

Cite as

Krishnendu Chatterjee, Luca de Alfaro, Rupak Majumdar, and Vishwanath Raman. Algorithms for Game Metrics. In IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 2, pp. 107-118, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2008)


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@InProceedings{chatterjee_et_al:LIPIcs.FSTTCS.2008.1745,
  author =	{Chatterjee, Krishnendu and de Alfaro, Luca and Majumdar, Rupak and Raman, Vishwanath},
  title =	{{Algorithms for Game Metrics}},
  booktitle =	{IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science},
  pages =	{107--118},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-08-8},
  ISSN =	{1868-8969},
  year =	{2008},
  volume =	{2},
  editor =	{Hariharan, Ramesh and Mukund, Madhavan and Vinay, V},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2008.1745},
  URN =		{urn:nbn:de:0030-drops-17455},
  doi =		{10.4230/LIPIcs.FSTTCS.2008.1745},
  annote =	{Keywords: Algorithms, Metrics, Kernel, Simulation, Bisimulation, Linear Programming, Theory of Reals}
}
Document
All-Norms and All-L_p-Norms Approximation Algorithms

Authors: Daniel Golovin, Anupam Gupta, Amit Kumar, and Kanat Tangwongsan

Published in: LIPIcs, Volume 2, IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (2008)


Abstract
In many optimization problems, a solution can be viewed as ascribing a ``cost\'\' to each client, and the goal is to optimize some aggregation of the per-client costs. We often optimize some $L_p$-norm (or some other symmetric convex function or norm) of the vector of costs---though different applications may suggest different norms to use. Ideally, we could obtain a solution that optimizes several norms simultaneously. In this paper, we examine approximation algorithms that simultaneously perform well on all norms, or on all $L_p$ norms. A natural problem in this framework is the $L_p$ Set Cover problem, which generalizes \textsc{Set Cover} and \textsc{Min-Sum Set Cover}. We show that the greedy algorithm \emph{simultaneously gives a $(p + \ln p + O(1))$-approximation for all $p$, and show that this approximation ratio is optimal up to constants} under reasonable complexity-theoretic assumptions. We additionally show how to use our analysis techniques to give similar results for the more general \emph{submodular set cover}, and prove some results for the so-called \emph{pipelined set cover} problem. We then go on to examine approximation algorithms in the ``all-norms\'\' and the ``all-$L_p$-norms\'\' frameworks more broadly, and present algorithms and structural results for other problems such as $k$-facility-location, TSP, and average flow-time minimization, extending and unifying previously known results.

Cite as

Daniel Golovin, Anupam Gupta, Amit Kumar, and Kanat Tangwongsan. All-Norms and All-L_p-Norms Approximation Algorithms. In IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 2, pp. 199-210, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2008)


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@InProceedings{golovin_et_al:LIPIcs.FSTTCS.2008.1753,
  author =	{Golovin, Daniel and Gupta, Anupam and Kumar, Amit and Tangwongsan, Kanat},
  title =	{{All-Norms and All-L\underlinep-Norms Approximation Algorithms}},
  booktitle =	{IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science},
  pages =	{199--210},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-08-8},
  ISSN =	{1868-8969},
  year =	{2008},
  volume =	{2},
  editor =	{Hariharan, Ramesh and Mukund, Madhavan and Vinay, V},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2008.1753},
  URN =		{urn:nbn:de:0030-drops-17537},
  doi =		{10.4230/LIPIcs.FSTTCS.2008.1753},
  annote =	{Keywords: Approximation algorithms, set-cover problems, combinatorial optimization, sampling minkowski norms}
}
Document
An Optimal Construction of Finite Automata from Regular Expressions

Authors: Stefan Gulan and Henning Fernau

Published in: LIPIcs, Volume 2, IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (2008)


Abstract
We consider the construction of finite automata from their corresponding regular expressions by a series of digraph-transformations along the expression\'s structure. Each intermediate graph represents an extended finite automaton accepting the same language. The character of our construction allows a fine-grained analysis of the emerging automaton\'s size, eventually leading to an optimality result.

Cite as

Stefan Gulan and Henning Fernau. An Optimal Construction of Finite Automata from Regular Expressions. In IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science. Leibniz International Proceedings in Informatics (LIPIcs), Volume 2, pp. 211-222, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2008)


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@InProceedings{gulan_et_al:LIPIcs.FSTTCS.2008.1754,
  author =	{Gulan, Stefan and Fernau, Henning},
  title =	{{An Optimal Construction of Finite Automata from Regular Expressions}},
  booktitle =	{IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science},
  pages =	{211--222},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-08-8},
  ISSN =	{1868-8969},
  year =	{2008},
  volume =	{2},
  editor =	{Hariharan, Ramesh and Mukund, Madhavan and Vinay, V},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2008.1754},
  URN =		{urn:nbn:de:0030-drops-17544},
  doi =		{10.4230/LIPIcs.FSTTCS.2008.1754},
  annote =	{Keywords: Finite automata,regular expressions,descriptional complexity}
}
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