Affiliation:
1. University of Toronto, Canada
2. Princeton University, USA
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.
Funder
Natural Sciences and Engineering Research Council of Canada
Ontario Ministry of Research
Publisher
Association for Computing Machinery (ACM)
Subject
Safety, Risk, Reliability and Quality,Software
Cited by
13 articles.
订阅此论文施引文献
订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献
1. Solving Infinite-State Games via Acceleration;Proceedings of the ACM on Programming Languages;2024-01-05
2. Church synthesis on register automata over linearly ordered data domains;Formal Methods in System Design;2023-10-10
3. Symbolic Fixpoint Algorithms for Logical LTL Games;2023 38th IEEE/ACM International Conference on Automated Software Engineering (ASE);2023-09-11
4. Boolean Abstractions for Realizability Modulo Theories;Computer Aided Verification;2023
5. Software model-checking as cyclic-proof search;Proceedings of the ACM on Programming Languages;2022-01-12