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Strategy synthesis for linear arithmetic games

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Zachary KincaidAuthors Info & Claims

Proceedings of the ACM on Programming Languages, Volume 2, Issue POPL

Article No.: 61, Pages 1 - 30

https://doi.org/10.1145/3158149

Published: 27 December 2017 Publication History

Abstract

Many problems in formal methods can be formalized as two-player games. For several applications—program synthesis, for example—in addition to determining which player wins the game, we are interested in computing a winning strategy for that player. This paper studies the strategy synthesis problem for games defined within the theory of linear rational arithmetic. Two types of games are considered. A satisfiability game, described by a quantified formula, is played by two players that take turns instantiating quantifiers. The objective of each player is to prove (or disprove) satisfiability of the formula. A reachability game, described by a pair of formulas defining the legal moves of each player, is played by two players that take turns choosing positions—rational vectors of some fixed dimension. The objective of each player is to reach a position where the opposing player has no legal moves (or to play the game forever). We give a complete algorithm for synthesizing winning strategies for satisfiability games and a sound (but necessarily incomplete) algorithm for synthesizing winning strategies for reachability games.

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Cited By

Fang LYang MCheng DHao YGuan QXiong LDastani MSichman JAlechina NDignum V(2024)Generalized Strategy Synthesis of Infinite-state Impartial Combinatorial Games via Exact Binary ClassificationProceedings of the 23rd International Conference on Autonomous Agents and Multiagent Systems10.5555/3635637.3662907(562-570)Online publication date: 6-May-2024
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
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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Index Terms

Strategy synthesis for linear arithmetic games
1. Software and its engineering
  1. Software creation and management
    1. Software development techniques
      1. Automatic programming
2. Theory of computation
  1. Logic
    1. Automated reasoning

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Published In

cover image Proceedings of the ACM on Programming Languages

Proceedings of the ACM on Programming Languages Volume 2, Issue POPL

January 2018

1961 pages

EISSN:2475-1421

DOI:10.1145/3177123

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Copyright © 2017 Owner/Author.

Permission to make digital or hard copies of part or all of this work for personal or classroom use is granted without fee provided that copies are not made or distributed for profit or commercial advantage and that copies bear this notice and the full citation on the first page. Copyrights for third-party components of this work must be honored. For all other uses, contact the Owner/Author.

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Association for Computing Machinery

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Publication History

Published: 27 December 2017

Published in PACMPL Volume 2, Issue POPL

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Cited By

Fang LYang MCheng DHao YGuan QXiong LDastani MSichman JAlechina NDignum V(2024)Generalized Strategy Synthesis of Infinite-state Impartial Combinatorial Games via Exact Binary ClassificationProceedings of the 23rd International Conference on Autonomous Agents and Multiagent Systems10.5555/3635637.3662907(562-570)Online publication date: 6-May-2024
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
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
Jakubův JJanota MUrban J(2024)Solving Hard Mizar Problems with Instantiation and Strategy InventionIntelligent Computer Mathematics10.1007/978-3-031-66997-2_18(315-333)Online publication date: 29-Jul-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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Murphy CKincaid Z(2024)Quantified Linear Arithmetic Satisfiability via Fine-Grained Strategy ImprovementComputer Aided Verification10.1007/978-3-031-65627-9_5(89-109)Online publication date: 26-Jul-2024
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