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FOCS '97 Proceedings of the 38th Annual Symposium on Foundations of Computer Science
EMSOFT '02 Proceedings of the Second International Conference on Embedded Software
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HSCC '02 Proceedings of the 5th International Workshop on Hybrid Systems: Computation and Control
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ICESS '07 Proceedings of the 3rd international conference on Embedded Software and Systems
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HSCC '08 Proceedings of the 11th international workshop on Hybrid Systems: Computation and Control
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Information and Computation
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Formal Methods in System Design
Specifications for decidable hybrid games
Theoretical Computer Science
LPAR'06 Proceedings of the 13th international conference on Logic for Programming, Artificial Intelligence, and Reasoning
FORMATS'05 Proceedings of the Third international conference on Formal Modeling and Analysis of Timed Systems
Optimal strategies in priced timed game automata
FSTTCS'04 Proceedings of the 24th international conference on Foundations of Software Technology and Theoretical Computer Science
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Proceedings of the 15th ACM international conference on Hybrid Systems: Computation and Control
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WADT'10 Proceedings of the 20th international conference on Recent Trends in Algebraic Development Techniques
Solving games via three-valued abstraction refinement
CONCUR'07 Proceedings of the 18th international conference on Concurrency Theory
A constraint-based approach to solving games on infinite graphs
Proceedings of the 41st ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages
Computable fixpoints in well-structured symbolic model checking
Formal Methods in System Design
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A procedure for the analysis of state spaces is called symbolic if it manipulates not individual states, but sets of states that are represented by constraints. Such a procedure can be used for the analysis of infinite state spaces, provided termination is guaranteed. We present symbolic procedures, and corresponding termination criteria, for the solution of infinite-state games, which occur in the control and modular verification of infinite-state systems. To characterize the termination of symbolic procedures for solving infinite-state games, we classify these game structures into four increasingly restrictive categories: 1. Class 1 consists of infinite-state structures for which all safety and reachability games can be solved. 2. Class 2 consists of infinite-state structures for which all ω-regular games can be solved. 3. Class 3 consists of infinite-state structures for which all nested positive boolean combinations of ω-regular games can be solved. 4. Class 4 consists of infinite-state structures for which all nested boolean combinations of ω-regular games can be solved. We give a structural characterization for each class, using equivalence relations on the state spaces of games which range from game versions of trace equivalence to a game version of bisimilarity. We provide infinite-state examples for all four classes of games from control problems for hybrid systems. We conclude by presenting symbolic algorithms for the synthesis of winning strategies ("controller synthesis") for infinite-state games with arbitrary u-regular objectives, and prove termination over all class-2 structures. This settles, in particular, the symbolic controller synthesis problem for rectangular hybrid systems.