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Volume

LIPIcs, Volume 82

26th EACSL Annual Conference on Computer Science Logic (CSL 2017)

CSL 2017, August 20-24, 2017, Stockholm, Sweden

Editors: Valentin Goranko and Mads Dam

Document

DOI: 10.4230/LIPIcs.ITP.2024.28

Lean Formalization of Completeness Proof for Coalition Logic with Common Knowledge

Authors: Kai Obendrauf, Anne Baanen, Patrick Koopmann, and Vera Stebletsova

Published in: LIPIcs, Volume 309, 15th International Conference on Interactive Theorem Proving (ITP 2024)

Abstract

Coalition Logic (CL) is a well-known formalism for reasoning about the strategic abilities of groups of agents in multi-agent systems. Coalition Logic with Common Knowledge (CLC) extends CL with operators from epistic logics, and thus with the ability to model the individual and common knowledge of agents. We have formalized the syntax and semantics of both logics in the interactive theorem prover Lean 4, and used it to prove soundness and completeness of its axiomatization. Our formalization uses the type class system to generalize over different aspects of CLC, thus allowing us to reuse some of to prove properties in related logics such as CL and CLK (CL with individual knowledge).

Cite as

Kai Obendrauf, Anne Baanen, Patrick Koopmann, and Vera Stebletsova. Lean Formalization of Completeness Proof for Coalition Logic with Common Knowledge. In 15th International Conference on Interactive Theorem Proving (ITP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 309, pp. 28:1-28:18, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{obendrauf_et_al:LIPIcs.ITP.2024.28,
  author =	{Obendrauf, Kai and Baanen, Anne and Koopmann, Patrick and Stebletsova, Vera},
  title =	{{Lean Formalization of Completeness Proof for Coalition Logic with Common Knowledge}},
  booktitle =	{15th International Conference on Interactive Theorem Proving (ITP 2024)},
  pages =	{28:1--28:18},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-337-9},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{309},
  editor =	{Bertot, Yves and Kutsia, Temur and Norrish, Michael},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ITP.2024.28},
  URN =		{urn:nbn:de:0030-drops-207560},
  doi =		{10.4230/LIPIcs.ITP.2024.28},
  annote =	{Keywords: Multi-agent systems, Coalition Logic, Epistemic Logic, common knowledge, completeness, formal methods, Lean prover}
}

Document

DOI: 10.4230/LIPIcs.CONCUR.2024.23

Regular Games with Imperfect Information Are Not That Regular

Authors: Laurent Doyen and Thomas Soullard

Published in: LIPIcs, Volume 311, 35th International Conference on Concurrency Theory (CONCUR 2024)

Abstract

We consider two-player games with imperfect information and the synthesis of a randomized strategy for one player that ensures the objective is satisfied almost-surely (i.e., with probability 1), regardless of the strategy of the other player. Imperfect information is modeled by an indistinguishability relation describing the pairs of histories that the first player cannot distinguish, a generalization of the traditional model with partial observations. The game is regular if it admits a regular function whose kernel commutes with the indistinguishability relation. The synthesis of pure strategies that ensure all possible outcomes satisfy the objective is possible in regular games, by a generic reduction that holds for all objectives. While the solution for pure strategies extends to randomized strategies in the traditional model with partial observations (which is always regular), a similar reduction does not exist in the more general model. Despite that, we show that in regular games with Büchi objectives the synthesis problem is decidable for randomized strategies that ensure the outcome satisfies the objective almost-surely.

Cite as

Laurent Doyen and Thomas Soullard. Regular Games with Imperfect Information Are Not That Regular. In 35th International Conference on Concurrency Theory (CONCUR 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 311, pp. 23:1-23:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{doyen_et_al:LIPIcs.CONCUR.2024.23,
  author =	{Doyen, Laurent and Soullard, Thomas},
  title =	{{Regular Games with Imperfect Information Are Not That Regular}},
  booktitle =	{35th International Conference on Concurrency Theory (CONCUR 2024)},
  pages =	{23:1--23:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-339-3},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{311},
  editor =	{Majumdar, Rupak and Silva, Alexandra},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CONCUR.2024.23},
  URN =		{urn:nbn:de:0030-drops-207953},
  doi =		{10.4230/LIPIcs.CONCUR.2024.23},
  annote =	{Keywords: Imperfect-information games, randomized strategies, synthesis}
}

Document

DOI: 10.4230/LIPIcs.FSCD.2024.14

Two-Dimensional Kripke Semantics I: Presheaves

Authors: G. A. Kavvos

Published in: LIPIcs, Volume 299, 9th International Conference on Formal Structures for Computation and Deduction (FSCD 2024)

Abstract

The study of modal logic has witnessed tremendous development following the introduction of Kripke semantics. However, recent developments in programming languages and type theory have led to a second way of studying modalities, namely through their categorical semantics. We show how the two correspond.

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G. A. Kavvos. Two-Dimensional Kripke Semantics I: Presheaves. In 9th International Conference on Formal Structures for Computation and Deduction (FSCD 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 299, pp. 14:1-14:23, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{kavvos:LIPIcs.FSCD.2024.14,
  author =	{Kavvos, G. A.},
  title =	{{Two-Dimensional Kripke Semantics I: Presheaves}},
  booktitle =	{9th International Conference on Formal Structures for Computation and Deduction (FSCD 2024)},
  pages =	{14:1--14:23},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-323-2},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{299},
  editor =	{Rehof, Jakob},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2024.14},
  URN =		{urn:nbn:de:0030-drops-203438},
  doi =		{10.4230/LIPIcs.FSCD.2024.14},
  annote =	{Keywords: modal logic, categorical semantics, Kripke semantics, duality, open maps}
}

Document

Track B: Automata, Logic, Semantics, and Theory of Programming

DOI: 10.4230/LIPIcs.ICALP.2024.127

Decidability of Graph Neural Networks via Logical Characterizations

Authors: Michael Benedikt, Chia-Hsuan Lu, Boris Motik, and Tony Tan

Published in: LIPIcs, Volume 297, 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)

Abstract

We present results concerning the expressiveness and decidability of a popular graph learning formalism, graph neural networks (GNNs), exploiting connections with logic. We use a family of recently-discovered decidable logics involving "Presburger quantifiers". We show how to use these logics to measure the expressiveness of classes of GNNs, in some cases getting exact correspondences between the expressiveness of logics and GNNs. We also employ the logics, and the techniques used to analyze them, to obtain decision procedures for verification problems over GNNs. We complement this with undecidability results for static analysis problems involving the logics, as well as for GNN verification problems.

Cite as

Michael Benedikt, Chia-Hsuan Lu, Boris Motik, and Tony Tan. Decidability of Graph Neural Networks via Logical Characterizations. In 51st International Colloquium on Automata, Languages, and Programming (ICALP 2024). Leibniz International Proceedings in Informatics (LIPIcs), Volume 297, pp. 127:1-127:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2024)

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@InProceedings{benedikt_et_al:LIPIcs.ICALP.2024.127,
  author =	{Benedikt, Michael and Lu, Chia-Hsuan and Motik, Boris and Tan, Tony},
  title =	{{Decidability of Graph Neural Networks via Logical Characterizations}},
  booktitle =	{51st International Colloquium on Automata, Languages, and Programming (ICALP 2024)},
  pages =	{127:1--127:20},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-322-5},
  ISSN =	{1868-8969},
  year =	{2024},
  volume =	{297},
  editor =	{Bringmann, Karl and Grohe, Martin and Puppis, Gabriele and Svensson, Ola},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.ICALP.2024.127},
  URN =		{urn:nbn:de:0030-drops-202708},
  doi =		{10.4230/LIPIcs.ICALP.2024.127},
  annote =	{Keywords: Logic, Graph Neural Networks}
}

Document

DOI: 10.4230/LIPIcs.FSCD.2023.23

Partial Model Checking and Partial Model Synthesis in LTL Using a Tableau-Based Approach

Authors: Serenella Cerrito, Valentin Goranko, and Sophie Paillocher

Published in: LIPIcs, Volume 260, 8th International Conference on Formal Structures for Computation and Deduction (FSCD 2023)

Abstract

In the process of designing a computer system S and checking whether an abstract model ℳ of S verifies a given specification property η, one might have only a partial knowledge of the model, either because ℳ has not yet been completely defined (constructed) by the designer, or because it is not completely observable by the verifier. This leads to new verification problems, subsuming satisfiability and model checking as special cases. We state and discuss these problems in the case of LTL specifications, and develop a uniform tableau-based approach for their solutions.

Cite as

Serenella Cerrito, Valentin Goranko, and Sophie Paillocher. Partial Model Checking and Partial Model Synthesis in LTL Using a Tableau-Based Approach. In 8th International Conference on Formal Structures for Computation and Deduction (FSCD 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 260, pp. 23:1-23:21, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023)

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@InProceedings{cerrito_et_al:LIPIcs.FSCD.2023.23,
  author =	{Cerrito, Serenella and Goranko, Valentin and Paillocher, Sophie},
  title =	{{Partial Model Checking and Partial Model Synthesis in LTL Using a Tableau-Based Approach}},
  booktitle =	{8th International Conference on Formal Structures for Computation and Deduction (FSCD 2023)},
  pages =	{23:1--23:21},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-277-8},
  ISSN =	{1868-8969},
  year =	{2023},
  volume =	{260},
  editor =	{Gaboardi, Marco and van Raamsdonk, Femke},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.FSCD.2023.23},
  URN =		{urn:nbn:de:0030-drops-180075},
  doi =		{10.4230/LIPIcs.FSCD.2023.23},
  annote =	{Keywords: Linear temporal logic LTL, partial transition systems, partial model checking, partial model synthesis, tableaux}
}

Document

DOI: 10.4230/LIPIcs.TIME.2019.13

Minimisation of Models Satisfying CTL Formulas

Authors: Serenella Cerrito, Amélie David, and Valentin Goranko

Published in: LIPIcs, Volume 147, 26th International Symposium on Temporal Representation and Reasoning (TIME 2019)

Abstract

We study the problem of minimisation of a given finite pointed Kripke model satisfying a given CTL formula, with the only objective to preserve the satisfaction of that formula in the resulting reduced model. We consider minimisations of the model with respect both to state-based redundancies and formula-based redundancies in that model. We develop a procedure computing all such minimisations, illustrate it with some examples, and provide some complexity analysis for it.

Cite as

Serenella Cerrito, Amélie David, and Valentin Goranko. Minimisation of Models Satisfying CTL Formulas. In 26th International Symposium on Temporal Representation and Reasoning (TIME 2019). Leibniz International Proceedings in Informatics (LIPIcs), Volume 147, pp. 13:1-13:15, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2019)

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@InProceedings{cerrito_et_al:LIPIcs.TIME.2019.13,
  author =	{Cerrito, Serenella and David, Am\'{e}lie and Goranko, Valentin},
  title =	{{Minimisation of Models Satisfying CTL Formulas}},
  booktitle =	{26th International Symposium on Temporal Representation and Reasoning (TIME 2019)},
  pages =	{13:1--13:15},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-127-6},
  ISSN =	{1868-8969},
  year =	{2019},
  volume =	{147},
  editor =	{Gamper, Johann and Pinchinat, Sophie and Sciavicco, Guido},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.TIME.2019.13},
  URN =		{urn:nbn:de:0030-drops-113718},
  doi =		{10.4230/LIPIcs.TIME.2019.13},
  annote =	{Keywords: CTL, model minimisation, bisimulation reduction, tableaux-based reduction}
}

Document

DOI: 10.4230/LIPIcs.TIME.2017.14

CTL with Finitely Bounded Semantics

Authors: Valentin Goranko, Antti Kuusisto, and Raine Rönnholm

Published in: LIPIcs, Volume 90, 24th International Symposium on Temporal Representation and Reasoning (TIME 2017)

Abstract

We consider a variation of the branching time logic CTL with non-standard, "finitely bounded" semantics (FBS). FBS is naturally defined as game-theoretic semantics where the proponent of truth of an eventuality must commit to a time limit (number of transition steps) within which the formula should become true on all (resp. some) paths starting from the state where the formula is evaluated. The resulting version CTL(FB) of CTL differs essentially from the standard one as it no longer has the finite model property. We develop two tableaux systems for CTL(FB). The first one deals with infinite sets of formulae, whereas the second one deals with finite sets of formulae in a slightly extended language allowing explicit indication of time limits in formulae. We prove soundness and completeness of both systems and also show that the latter tableaux system provides an EXPTIME decision procedure for it and thus prove EXPTIME-completeness of the satisfiability problem.

Cite as

Valentin Goranko, Antti Kuusisto, and Raine Rönnholm. CTL with Finitely Bounded Semantics. In 24th International Symposium on Temporal Representation and Reasoning (TIME 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 90, pp. 14:1-14:19, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{goranko_et_al:LIPIcs.TIME.2017.14,
  author =	{Goranko, Valentin and Kuusisto, Antti and R\"{o}nnholm, Raine},
  title =	{{CTL with Finitely Bounded Semantics}},
  booktitle =	{24th International Symposium on Temporal Representation and Reasoning (TIME 2017)},
  pages =	{14:1--14:19},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-052-1},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{90},
  editor =	{Schewe, Sven and Schneider, Thomas and Wijsen, Jef},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.TIME.2017.14},
  URN =		{urn:nbn:de:0030-drops-79325},
  doi =		{10.4230/LIPIcs.TIME.2017.14},
  annote =	{Keywords: CTL, finitely bounded semantics, tableaux, decidability}
}

Document

Complete Volume

DOI: 10.4230/LIPIcs.CSL.2017

LIPIcs, Volume 82, CSL'17, Complete Volume

Authors: Valentin Goranko and Mads Dam

Published in: LIPIcs, Volume 82, 26th EACSL Annual Conference on Computer Science Logic (CSL 2017)

Abstract

LIPIcs, Volume 82, CSL'17, Complete Volume

Cite as

26th EACSL Annual Conference on Computer Science Logic (CSL 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 82, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@Proceedings{goranko_et_al:LIPIcs.CSL.2017,
  title =	{{LIPIcs, Volume 82, CSL'17, Complete Volume}},
  booktitle =	{26th EACSL Annual Conference on Computer Science Logic (CSL 2017)},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-045-3},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{82},
  editor =	{Goranko, Valentin and Dam, Mads},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2017},
  URN =		{urn:nbn:de:0030-drops-78103},
  doi =		{10.4230/LIPIcs.CSL.2017},
  annote =	{Keywords: Conference Proceedings, Software/Program Verification, Formal Definitions and Theory, Language Constructs and Features, Theory of Computation}
}

Document

Front Matter

DOI: 10.4230/LIPIcs.CSL.2017.0

Front Matter, Table of Contents, Preface, Conference Organization, External Reviewers

Authors: Valentin Goranko and Mads Dam

Published in: LIPIcs, Volume 82, 26th EACSL Annual Conference on Computer Science Logic (CSL 2017)

Abstract

Front Matter, Table of Contents, Preface, Conference Organization, External Reviewers

Cite as

26th EACSL Annual Conference on Computer Science Logic (CSL 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 82, pp. 0:i-0:xviii, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{goranko_et_al:LIPIcs.CSL.2017.0,
  author =	{Goranko, Valentin and Dam, Mads},
  title =	{{Front Matter, Table of Contents, Preface, Conference Organization, External Reviewers}},
  booktitle =	{26th EACSL Annual Conference on Computer Science Logic (CSL 2017)},
  pages =	{0:i--0:xviii},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-045-3},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{82},
  editor =	{Goranko, Valentin and Dam, Mads},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2017.0},
  URN =		{urn:nbn:de:0030-drops-76671},
  doi =		{10.4230/LIPIcs.CSL.2017.0},
  annote =	{Keywords: Front Matter, Table of Contents, Preface, Conference Organization, External Reviewers}
}

Document

DOI: 10.4230/LIPIcs.CSL.2017.1

The Ackermann Award 2017

Authors: Anuj Dawar and Daniel Leivant

Published in: LIPIcs, Volume 82, 26th EACSL Annual Conference on Computer Science Logic (CSL 2017)

Abstract

The Ackermann Award is the EACSL Outstanding Dissertation Award for Logic in Computer Science. It is presented during the annual conference of the EACSL (CSL'xx). This contribution reports on the 2017 edition of the award.

Cite as

Anuj Dawar and Daniel Leivant. The Ackermann Award 2017. In 26th EACSL Annual Conference on Computer Science Logic (CSL 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 82, pp. 1:1-1:4, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{dawar_et_al:LIPIcs.CSL.2017.1,
  author =	{Dawar, Anuj and Leivant, Daniel},
  title =	{{The Ackermann Award 2017}},
  booktitle =	{26th EACSL Annual Conference on Computer Science Logic (CSL 2017)},
  pages =	{1:1--1:4},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-045-3},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{82},
  editor =	{Goranko, Valentin and Dam, Mads},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2017.1},
  URN =		{urn:nbn:de:0030-drops-76938},
  doi =		{10.4230/LIPIcs.CSL.2017.1},
  annote =	{Keywords: Ackermann Award, jury report, citation}
}

Document

Invited Talk

DOI: 10.4230/LIPIcs.CSL.2017.2

Schema Mappings: Structural Properties and Limits (Invited Talk)

Authors: Phokion G. Kolaitis

Published in: LIPIcs, Volume 82, 26th EACSL Annual Conference on Computer Science Logic (CSL 2017)

Abstract

A schema mapping is a high-level specification of the relationship between two database schemas. For the past fifteen years, schema mappings have played an essential role in the modeling and analysis of important data inter-operability tasks, such as data exchange and data integration. Syntactically, schema mappings are expressed in some schema-mapping language, which, typically, is a fragment of first-order logic or second-order logic. In the first part of the talk, we will introduce the main schema-mapping languages, will discuss the fundamental structural properties of these languages, and will then use these structural properties to obtain characterizations of various schema-mapping languages in the spirit of abstract model theory. In the second part of the talk, we will examine schema mappings from a dynamic viewpoint by considering sequences of schema mappings and studying the convergence properties of such sequences. To this effect, we will introduce a metric space that is based on a natural notion of distance between sets of database instances and will investigate pointwise limits and uniform limits of sequences of schema mappings. Among other findings, it will turn out that the completion of this metric space can be described in terms of graph limits arising from converging sequences of homomorphism densities.

Cite as

Phokion G. Kolaitis. Schema Mappings: Structural Properties and Limits (Invited Talk). In 26th EACSL Annual Conference on Computer Science Logic (CSL 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 82, p. 2:1, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{kolaitis:LIPIcs.CSL.2017.2,
  author =	{Kolaitis, Phokion G.},
  title =	{{Schema Mappings: Structural Properties and Limits}},
  booktitle =	{26th EACSL Annual Conference on Computer Science Logic (CSL 2017)},
  pages =	{2:1--2:1},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-045-3},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{82},
  editor =	{Goranko, Valentin and Dam, Mads},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2017.2},
  URN =		{urn:nbn:de:0030-drops-76707},
  doi =		{10.4230/LIPIcs.CSL.2017.2},
  annote =	{Keywords: logic and databases, schema mappings, data exchange, metric spaces}
}

Document

Invited Talk

DOI: 10.4230/LIPIcs.CSL.2017.3

First-Order Interpolation and Grey Areas of Proofs (Invited Talk)

Authors: Laura Kovács

Published in: LIPIcs, Volume 82, 26th EACSL Annual Conference on Computer Science Logic (CSL 2017)

Abstract

Interpolation is an important technique in computer aided verification and static analysis of programs. In particular, interpolants extracted from so-called local proofs are used in invariant generation and bounded model checking. An interpolant extracted from such a proof is a boolean combination of formulas occurring in the proof. In this talk we first describe a technique of generating and optimizing interpolants based on transformations of what we call the “grey area” of local proofs. Local changes in proofs can change the extracted interpolant. Our method can describe properties of extracted interpolants obtained by such proof changes as a pseudo-boolean constraint. By optimizing solutions of this constraint we also improve the extracted interpolants. Unlike many other interpolation techniques, our technique is very general and applies to arbitrary theories. Our approach is implemented in the theorem prover Vampire and evaluated on a large number of benchmarks coming from first-order theorem proving and bounded model checking using logic with equality, uninterpreted functions and linear integer arithmetic. Our experiments demonstrate the power of the new techniques: for example, it is not unusual that our proof transformation gives more than a tenfold reduction in the size of interpolants. While local proofs admit efficient interpolation algorithms, standard complete proof systems, such as superposition, for theories having the interpolation property are not necessarily complete for local proofs. In this talk we therefore also investigate interpolant extraction from non-local proofs in the superposition calculus and prove a number of general results about interpolant extraction and complexity of extracted interpolants. In particular, we prove that the number of quantifier alternations in first-order interpolants of formulas without quantifier alternations is unbounded. This result has far-reaching consequences for using local proofs as a foundation for interpolating proof systems - any such proof system should deal with formulas of arbitrary quantifier complexity.

Cite as

Laura Kovács. First-Order Interpolation and Grey Areas of Proofs (Invited Talk). In 26th EACSL Annual Conference on Computer Science Logic (CSL 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 82, p. 3:1, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{kovacs:LIPIcs.CSL.2017.3,
  author =	{Kov\'{a}cs, Laura},
  title =	{{First-Order Interpolation and Grey Areas of Proofs}},
  booktitle =	{26th EACSL Annual Conference on Computer Science Logic (CSL 2017)},
  pages =	{3:1--3:1},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-045-3},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{82},
  editor =	{Goranko, Valentin and Dam, Mads},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2017.3},
  URN =		{urn:nbn:de:0030-drops-76912},
  doi =		{10.4230/LIPIcs.CSL.2017.3},
  annote =	{Keywords: theorem proving, interpolation, proof transformations, constraint solving, program analysis}
}

Document

Invited Talk

DOI: 10.4230/LIPIcs.CSL.2017.4

Current Trends and New Perspectives for First-Order Model Checking (Invited Talk)

Authors: Stephan Kreutzer

Published in: LIPIcs, Volume 82, 26th EACSL Annual Conference on Computer Science Logic (CSL 2017)

Abstract

The model-checking problem for a logic LLL is the problem of decidig for a given formula phi in LLL and structure AA whether the formula is true in the structure, i.e. whether AA models phi. Model-checking for logics such as First-Order Logic (FO) or Monadic Second-Order Logic (MSO) has been studied intensively in the literature, especially in the context of algorithmic meta-theorems within the framework of parameterized complexity. However, in the past the focus of this line of research was model-checking on classes of sparse graphs, e.g. planar graphs, graph classes excluding a minor or classes which are nowhere dense. By now, the complexity of first-order model-checking on sparse classes of graphs is completely understood. Hence, current research now focusses mainly on classes of dense graphs. In this talk we will briefly review the known results on sparse classes of graphs and explain the complete classification of classes of sparse graphs on which first-order model-checking is tractable. In the second part we will then focus on recent and ongoing research analysing the complexity of first-order model-checking on classes of dense graphs.

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Stephan Kreutzer. Current Trends and New Perspectives for First-Order Model Checking (Invited Talk). In 26th EACSL Annual Conference on Computer Science Logic (CSL 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 82, pp. 4:1-4:5, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{kreutzer:LIPIcs.CSL.2017.4,
  author =	{Kreutzer, Stephan},
  title =	{{Current Trends and New Perspectives for First-Order Model Checking}},
  booktitle =	{26th EACSL Annual Conference on Computer Science Logic (CSL 2017)},
  pages =	{4:1--4:5},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-045-3},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{82},
  editor =	{Goranko, Valentin and Dam, Mads},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2017.4},
  URN =		{urn:nbn:de:0030-drops-77095},
  doi =		{10.4230/LIPIcs.CSL.2017.4},
  annote =	{Keywords: Finite Model Theory, Computational Model Theory, Algorithmic Meta Theorems, Model-Checking, Logical Approaches in Graph Theory}
}

Document

Invited Talk

DOI: 10.4230/LIPIcs.CSL.2017.5

Arithmetic Circuits: An Overview (Invited Talk)

Authors: Meena Mahajan

Published in: LIPIcs, Volume 82, 26th EACSL Annual Conference on Computer Science Logic (CSL 2017)

Abstract

This talk reviews recent developments in algebraic complexity theory. It outlines some major results concerning structure, completeness, closure, and lower bounds. It describes some techniques that have been central to obtaining these results, including extreme depth reduction, partial derivatives, and padding.

Cite as

Meena Mahajan. Arithmetic Circuits: An Overview (Invited Talk). In 26th EACSL Annual Conference on Computer Science Logic (CSL 2017). Leibniz International Proceedings in Informatics (LIPIcs), Volume 82, p. 5:1, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2017)

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@InProceedings{mahajan:LIPIcs.CSL.2017.5,
  author =	{Mahajan, Meena},
  title =	{{Arithmetic Circuits: An Overview}},
  booktitle =	{26th EACSL Annual Conference on Computer Science Logic (CSL 2017)},
  pages =	{5:1--5:1},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-045-3},
  ISSN =	{1868-8969},
  year =	{2017},
  volume =	{82},
  editor =	{Goranko, Valentin and Dam, Mads},
  publisher =	{Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{https://drops.dagstuhl.de/entities/document/10.4230/LIPIcs.CSL.2017.5},
  URN =		{urn:nbn:de:0030-drops-76858},
  doi =		{10.4230/LIPIcs.CSL.2017.5},
  annote =	{Keywords: algebraic complexity, circuits, formulas, branching programs, determinant, permanent}
}

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