8 Search Results for "Murawski, Andrzej S."


Document
The Big-O Problem for Labelled Markov Chains and Weighted Automata

Authors: Dmitry Chistikov, Stefan Kiefer, Andrzej S. Murawski, and David Purser

Published in: LIPIcs, Volume 171, 31st International Conference on Concurrency Theory (CONCUR 2020)


Abstract
Given two weighted automata, we consider the problem of whether one is big-O of the other, i.e., if the weight of every finite word in the first is not greater than some constant multiple of the weight in the second. We show that the problem is undecidable, even for the instantiation of weighted automata as labelled Markov chains. Moreover, even when it is known that one weighted automaton is big-O of another, the problem of finding or approximating the associated constant is also undecidable. Our positive results show that the big-O problem is polynomial-time solvable for unambiguous automata, coNP-complete for unlabelled weighted automata (i.e., when the alphabet is a single character) and decidable, subject to Schanuel’s conjecture, when the language is bounded (i.e., a subset of w_1^* … w_m^* for some finite words w_1,… ,w_m). On labelled Markov chains, the problem can be restated as a ratio total variation distance, which, instead of finding the maximum difference between the probabilities of any two events, finds the maximum ratio between the probabilities of any two events. The problem is related to ε-differential privacy, for which the optimal constant of the big-O notation is exactly exp(ε).

Cite as

Dmitry Chistikov, Stefan Kiefer, Andrzej S. Murawski, and David Purser. The Big-O Problem for Labelled Markov Chains and Weighted Automata. In 31st International Conference on Concurrency Theory (CONCUR 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 171, pp. 41:1-41:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020)


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@InProceedings{chistikov_et_al:LIPIcs.CONCUR.2020.41,
  author =	{Chistikov, Dmitry and Kiefer, Stefan and Murawski, Andrzej S. and Purser, David},
  title =	{{The Big-O Problem for Labelled Markov Chains and Weighted Automata}},
  booktitle =	{31st International Conference on Concurrency Theory (CONCUR 2020)},
  pages =	{41:1--41:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-160-3},
  ISSN =	{1868-8969},
  year =	{2020},
  volume =	{171},
  editor =	{Konnov, Igor and Kov\'{a}cs, Laura},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CONCUR.2020.41},
  URN =		{urn:nbn:de:0030-drops-128534},
  doi =		{10.4230/LIPIcs.CONCUR.2020.41},
  annote =	{Keywords: weighted automata, labelled Markov chains, probabilistic systems}
}
Document
On the Expressivity of Linear Recursion Schemes

Authors: Pierre Clairambault and Andrzej S. Murawski

Published in: LIPIcs, Volume 138, 44th International Symposium on Mathematical Foundations of Computer Science (MFCS 2019)


Abstract
We investigate the expressive power of higher-order recursion schemes (HORS) restricted to linear types. Two formalisms are considered: multiplicative additive HORS (MAHORS), which feature both linear function types and products, and multiplicative HORS (MHORS), based on linear function types only. For MAHORS, we establish an equi-expressivity result with a variant of tree-stack automata. Consequently, we can show that MAHORS are strictly more expressive than first-order HORS, that they are incomparable with second-order HORS, and that the associated branch languages lie at the third level of the collapsible pushdown hierarchy. In the multiplicative case, we show that MHORS are equivalent to a special kind of pushdown automata. It follows that any MHORS can be translated to an equivalent first-order MHORS in polynomial time. Further, we show that MHORS generate regular trees and can be translated to equivalent order-0 HORS in exponential time. Consequently, MHORS turn out to have the same expressive power as 0-HORS but they can be exponentially more concise. Our results are obtained through a combination of techniques from game semantics, the geometry of interaction and automata theory.

Cite as

Pierre Clairambault and Andrzej S. Murawski. On the Expressivity of Linear Recursion Schemes. In 44th International Symposium on Mathematical Foundations of Computer Science (MFCS 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 138, pp. 50:1-50:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)


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@InProceedings{clairambault_et_al:LIPIcs.MFCS.2019.50,
  author =	{Clairambault, Pierre and Murawski, Andrzej S.},
  title =	{{On the Expressivity of Linear Recursion Schemes}},
  booktitle =	{44th International Symposium on Mathematical Foundations of Computer Science (MFCS 2019)},
  pages =	{50:1--50:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-117-7},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{138},
  editor =	{Rossmanith, Peter and Heggernes, Pinar and Katoen, Joost-Pieter},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2019.50},
  URN =		{urn:nbn:de:0030-drops-109945},
  doi =		{10.4230/LIPIcs.MFCS.2019.50},
  annote =	{Keywords: higher-order recursion schemes, linear logic, game semantics, geometry of interaction}
}
Document
Asymmetric Distances for Approximate Differential Privacy

Authors: Dmitry Chistikov, Andrzej S. Murawski, and David Purser

Published in: LIPIcs, Volume 140, 30th International Conference on Concurrency Theory (CONCUR 2019)


Abstract
Differential privacy is a widely studied notion of privacy for various models of computation, based on measuring differences between probability distributions. We consider (epsilon,delta)-differential privacy in the setting of labelled Markov chains. For a given epsilon, the parameter delta can be captured by a variant of the total variation distance, which we call lv_{alpha} (where alpha = e^{epsilon}). First we study lv_{alpha} directly, showing that it cannot be computed exactly. However, the associated approximation problem turns out to be in PSPACE and #P-hard. Next we introduce a new bisimilarity distance for bounding lv_{alpha} from above, which provides a tighter bound than previously known distances while remaining computable with the same complexity (polynomial time with an NP oracle). We also propose an alternative bound that can be computed in polynomial time. Finally, we illustrate the distances on case studies.

Cite as

Dmitry Chistikov, Andrzej S. Murawski, and David Purser. Asymmetric Distances for Approximate Differential Privacy. In 30th International Conference on Concurrency Theory (CONCUR 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 140, pp. 10:1-10:17, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)


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@InProceedings{chistikov_et_al:LIPIcs.CONCUR.2019.10,
  author =	{Chistikov, Dmitry and Murawski, Andrzej S. and Purser, David},
  title =	{{Asymmetric Distances for Approximate Differential Privacy}},
  booktitle =	{30th International Conference on Concurrency Theory (CONCUR 2019)},
  pages =	{10:1--10:17},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-121-4},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{140},
  editor =	{Fokkink, Wan and van Glabbeek, Rob},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CONCUR.2019.10},
  URN =		{urn:nbn:de:0030-drops-109121},
  doi =		{10.4230/LIPIcs.CONCUR.2019.10},
  annote =	{Keywords: Bisimilarity distances, Differential privacy, Labelled Markov chains}
}
Document
Polynomial-Time Equivalence Testing for Deterministic Fresh-Register Automata

Authors: Andrzej S. Murawski, Steven J. Ramsay, and Nikos Tzevelekos

Published in: LIPIcs, Volume 117, 43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018)


Abstract
Register automata are one of the most studied automata models over infinite alphabets. The complexity of language equivalence for register automata is quite subtle. In general, the problem is undecidable but, in the deterministic case, it is known to be decidable and in NP. Here we propose a polynomial-time algorithm building upon automata- and group-theoretic techniques. The algorithm is applicable to standard register automata with a fixed number of registers as well as their variants with a variable number of registers and ability to generate fresh data values (fresh-register automata). To complement our findings, we also investigate the associated inclusion problem and show that it is PSPACE-complete.

Cite as

Andrzej S. Murawski, Steven J. Ramsay, and Nikos Tzevelekos. Polynomial-Time Equivalence Testing for Deterministic Fresh-Register Automata. In 43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018). Leibniz International Proceedings in Informatics (LIPIcs), Volume 117, pp. 72:1-72:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2018)


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@InProceedings{murawski_et_al:LIPIcs.MFCS.2018.72,
  author =	{Murawski, Andrzej S. and Ramsay, Steven J. and Tzevelekos, Nikos},
  title =	{{Polynomial-Time Equivalence Testing for Deterministic Fresh-Register Automata}},
  booktitle =	{43rd International Symposium on Mathematical Foundations of Computer Science (MFCS 2018)},
  pages =	{72:1--72:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-086-6},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{117},
  editor =	{Potapov, Igor and Spirakis, Paul and Worrell, James},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.MFCS.2018.72},
  URN =		{urn:nbn:de:0030-drops-96544},
  doi =		{10.4230/LIPIcs.MFCS.2018.72},
  annote =	{Keywords: automata over infinite alphabets, language equivalence, bisimilarity, computational group theory}
}
Document
Higher-Order Linearisability

Authors: Andrzej S. Murawski and Nikos Tzevelekos

Published in: LIPIcs, Volume 85, 28th International Conference on Concurrency Theory (CONCUR 2017)


Abstract
Linearisability is a central notion for verifying concurrent libraries: a library is proven correct if its operational history can be rearranged into a sequential one that satisfies a given specification. Until now, linearisability has been examined for libraries in which method arguments and method results were of ground type. In this paper we extend linearisability to the general higher-order setting, where methods of arbitrary type can be passed as arguments and returned as values, and establish its soundness.

Cite as

Andrzej S. Murawski and Nikos Tzevelekos. Higher-Order Linearisability. In 28th International Conference on Concurrency Theory (CONCUR 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 85, pp. 34:1-34:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)


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@InProceedings{murawski_et_al:LIPIcs.CONCUR.2017.34,
  author =	{Murawski, Andrzej S. and Tzevelekos, Nikos},
  title =	{{Higher-Order Linearisability}},
  booktitle =	{28th International Conference on Concurrency Theory (CONCUR 2017)},
  pages =	{34:1--34:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-048-4},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{85},
  editor =	{Meyer, Roland and Nestmann, Uwe},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CONCUR.2017.34},
  URN =		{urn:nbn:de:0030-drops-78035},
  doi =		{10.4230/LIPIcs.CONCUR.2017.34},
  annote =	{Keywords: Linearisability, Concurrency, Higher-Order Computation}
}
Document
Böhm Trees as Higher-Order Recursive Schemes

Authors: Pierre Clairambault and Andrzej S. Murawski

Published in: LIPIcs, Volume 24, IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2013)


Abstract
Higher-order recursive schemes (HORS) are schematic representations of functional programs. They generate possibly infinite ranked labelled trees and, in that respect, are known to be equivalent to a restricted fragment of the lambda-Y-calculus consisting of ground-type terms whose free variables have types of the form o -> ... -> o (with o being a special case). In this paper, we show that any lambda-Y-term (with no restrictions on term type or the types of free variables) can actually be represented by a HORS. More precisely, for any lambda-Y-term M, there exists a HORS generating a tree that faithfully represents M's (eta-long) Böhm tree. In particular, the HORS captures higher-order binding information contained in the Böhm tree. An analogous result holds for finitary PCF. As a consequence, we can reduce a variety of problems related to the lambda-Y-calculus or finitary PCF to problems concerning higher-order recursive schemes. For instance, Böhm tree equivalence can be reduced to the equivalence problem for HORS. Our results also enable MSO model-checking of Böhm trees, despite the general undecidability of the problem.

Cite as

Pierre Clairambault and Andrzej S. Murawski. Böhm Trees as Higher-Order Recursive Schemes. In IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2013). Leibniz International Proceedings in Informatics (LIPIcs), Volume 24, pp. 91-102, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2013)


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@InProceedings{clairambault_et_al:LIPIcs.FSTTCS.2013.91,
  author =	{Clairambault, Pierre and Murawski, Andrzej S.},
  title =	{{B\"{o}hm Trees as Higher-Order Recursive Schemes}},
  booktitle =	{IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2013)},
  pages =	{91--102},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-939897-64-4},
  ISSN =	{1868-8969},
  year =	{2013},
  volume =	{24},
  editor =	{Seth, Anil and Vishnoi, Nisheeth K.},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSTTCS.2013.91},
  URN =		{urn:nbn:de:0030-drops-43644},
  doi =		{10.4230/LIPIcs.FSTTCS.2013.91},
  annote =	{Keywords: Lambda calculus, B\"{o}hm trees, Recursion Schemes}
}
Document
10252 Abstracts Collection – Game Semantics and Program Verification

Authors: Paul-Andre Mellies, Andrzej S. Murawski, Andrea Schalk, and Igor Walukiewicz

Published in: Dagstuhl Seminar Proceedings, Volume 10252, Game Semantics and Program Verification (2010)


Abstract
From 20th to 25th June 2010, the Dagstuhl Seminar "Game Semantics and Program Verification'' was held in Schloss Dagstuhl - Leibniz Center for Informatics. During the seminar, several participants presented their current research, and ongoing work and open problems were discussed. Abstracts of the presentations given during the seminar as well as abstracts of seminar results and ideas are put together in this paper. The first section describes the seminar topics and goals in general. Links to extended abstracts or full papers are provided, if available.

Cite as

Paul-Andre Mellies, Andrzej S. Murawski, Andrea Schalk, and Igor Walukiewicz. 10252 Abstracts Collection – Game Semantics and Program Verification. In Game Semantics and Program Verification. Dagstuhl Seminar Proceedings, Volume 10252, pp. 1-11, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2010)


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@InProceedings{mellies_et_al:DagSemProc.10252.1,
  author =	{Mellies, Paul-Andre and Murawski, Andrzej S. and Schalk, Andrea and Walukiewicz, Igor},
  title =	{{10252 Abstracts Collection – Game Semantics and Program Verification}},
  booktitle =	{Game Semantics and Program Verification},
  pages =	{1--11},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2010},
  volume =	{10252},
  editor =	{Paul-Andre Mellies and Andrzej S. Murawski and Andrea Schalk and Igor Walukiewicz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagSemProc.10252.1},
  URN =		{urn:nbn:de:0030-drops-27945},
  doi =		{10.4230/DagSemProc.10252.1},
  annote =	{Keywords: Software verification, Semantics of programming languages, Game semantics, Static analysis, Model checking}
}
Document
10252 Executive Summary – Game Semantics and Program Verification

Authors: Paul-Andre Mellies, Andrzej S. Murawski, Andrea Schalk, and Igor Walukiewicz

Published in: Dagstuhl Seminar Proceedings, Volume 10252, Game Semantics and Program Verification (2010)


Abstract
The seminar took place from 20th until 25th June 2010. Its primary aim was to foster interaction between researchers working on modelling programs/proofs using games and the verification community. The meeting brought together 28 researchers from eight different countries, both junior and senior, for a systematic assessment of what the two areas have to offer to one another, critical evaluation of what has been achieved so far, with a view to establishing common research goals for the future.

Cite as

Paul-Andre Mellies, Andrzej S. Murawski, Andrea Schalk, and Igor Walukiewicz. 10252 Executive Summary – Game Semantics and Program Verification. In Game Semantics and Program Verification. Dagstuhl Seminar Proceedings, Volume 10252, pp. 1-5, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2010)


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@InProceedings{mellies_et_al:DagSemProc.10252.2,
  author =	{Mellies, Paul-Andre and Murawski, Andrzej S. and Schalk, Andrea and Walukiewicz, Igor},
  title =	{{10252 Executive Summary – Game Semantics and Program Verification}},
  booktitle =	{Game Semantics and Program Verification},
  pages =	{1--5},
  series =	{Dagstuhl Seminar Proceedings (DagSemProc)},
  ISSN =	{1862-4405},
  year =	{2010},
  volume =	{10252},
  editor =	{Paul-Andre Mellies and Andrzej S. Murawski and Andrea Schalk and Igor Walukiewicz},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/DagSemProc.10252.2},
  URN =		{urn:nbn:de:0030-drops-27938},
  doi =		{10.4230/DagSemProc.10252.2},
  annote =	{Keywords: Software verification, Semantics of programming languages, Game semantics, Static analysis, Model checking}
}
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