research-article

A constraint-based approach to solving games on infinite graphs

Authors:

Tewodros Beyene,

Swarat Chaudhuri,

Corneliu Popeea,

Andrey RybalchenkoAuthors Info & Claims

POPL '14: Proceedings of the 41st ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages

Pages 221 - 233

https://doi.org/10.1145/2535838.2535860

Published: 08 January 2014 Publication History

Abstract

We present a constraint-based approach to computing winning strategies in two-player graph games over the state space of infinite-state programs. Such games have numerous applications in program verification and synthesis, including the synthesis of infinite-state reactive programs and branching-time verification of infinite-state programs. Our method handles games with winning conditions given by safety, reachability, and general Linear Temporal Logic (LTL) properties. For each property class, we give a deductive proof rule that --- provided a symbolic representation of the game players --- describes a winning strategy for a particular player. Our rules are sound and relatively complete. We show that these rules can be automated by using an off-the-shelf Horn constraint solver that supports existential quantification in clause heads. The practical promise of the rules is demonstrated through several case studies, including a challenging "Cinderella-Stepmother game" that allows infinite alternation of discrete and continuous choices by two players, as well as examples derived from prior work on program repair and synthesis.

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A constraint-based approach to solving games on infinite graphs

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cover image ACM Conferences

POPL '14: Proceedings of the 41st ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages

January 2014

702 pages

ISBN:9781450325448

DOI:10.1145/2535838

General Chair:
Suresh Jagannathan
Purdue University, USA
,
Program Chair:
Peter Sewell
University of Cambridge, UK

ACM SIGPLAN Notices Volume 49, Issue 1
POPL '14
January 2014
661 pages
ISSN:0362-1340
EISSN:1558-1160
DOI:10.1145/2578855
Editor:
Mark W. Bailey
Hamilton College, Clinton, NY
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Published: 08 January 2014

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January 22 - 24, 2014

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Cited By

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https://dl.acm.org/doi/10.5555/3635637.3662907
Heim PDimitrova R(2024)Solving Infinite-State Games via AccelerationProceedings of the ACM on Programming Languages10.1145/36328998:POPL(1696-1726)Online publication date: 5-Jan-2024
https://dl.acm.org/doi/10.1145/3632899
Zhang XLi BCai SRoychoudhury APaiva AAbreu RStorey M(2024)Deep Combination of CDCL(T) and Local Search for Satisfiability Modulo Non-Linear Integer Arithmetic TheoryProceedings of the IEEE/ACM 46th International Conference on Software Engineering10.1145/3597503.3639105(1-13)Online publication date: 20-May-2024
https://dl.acm.org/doi/10.1145/3597503.3639105
Rodríguez ASánchez C(2024)Realizability Modulo TheoriesJournal of Logical and Algebraic Methods in Programming10.1016/j.jlamp.2024.100971(100971)Online publication date: May-2024
https://doi.org/10.1016/j.jlamp.2024.100971
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Maderbacher BWindisch FBloem R(2024)Synthesis from Infinite-State Generalized Reactivity(1) SpecificationsLeveraging Applications of Formal Methods, Verification and Validation. Software Engineering Methodologies10.1007/978-3-031-75387-9_17(281-301)Online publication date: 27-Oct-2024
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Schmuck AHeim PDimitrova RNayak S(2024)Localized Attractor Computations for Infinite-State GamesComputer Aided Verification10.1007/978-3-031-65633-0_7(135-158)Online publication date: 24-Jul-2024
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