Infinite games on finitely coloured graphs with applications to automata on infinite trees
Theoretical Computer Science
Efficient minimization of deterministic weak &ohgr;-automata
Information Processing Letters
Switching and Finite Automata Theory: Computer Science Series
Switching and Finite Automata Theory: Computer Science Series
Infinite Games and Verification (Extended Abstract of a Tutorial)
CAV '02 Proceedings of the 14th International Conference on Computer Aided Verification
How much memory is needed to win infinite games?
LICS '97 Proceedings of the 12th Annual IEEE Symposium on Logic in Computer Science
STOC '82 Proceedings of the fourteenth annual ACM symposium on Theory of computing
An n log n algorithm for minimizing states in a finite automaton
An n log n algorithm for minimizing states in a finite automaton
A Landscape with Games in the Background
LICS '04 Proceedings of the 19th Annual IEEE Symposium on Logic in Computer Science
Fair Simulation Relations, Parity Games, and State Space Reduction for Büchi Automata
SIAM Journal on Computing
Infinite sequences and finite machines
SWCT '63 Proceedings of the 1963 Proceedings of the Fourth Annual Symposium on Switching Circuit Theory and Logical Design
Symbolic synthesis of finite-state controllers for request-response specifications
CIAA'03 Proceedings of the 8th international conference on Implementation and application of automata
Simulation relations for alternating parity automata and parity games
DLT'06 Proceedings of the 10th international conference on Developments in Language Theory
Optimizing winning strategies in regular infinite games
SOFSEM'08 Proceedings of the 34th conference on Current trends in theory and practice of computer science
Small strategies for safety games
ATVA'11 Proceedings of the 9th international conference on Automated technology for verification and analysis
Strategy machines and their complexity
MFCS'12 Proceedings of the 37th international conference on Mathematical Foundations of Computer Science
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We deal with the problem of reducing the memory necessary for implementing winning strategies in infinite games. We present an algorithm that is based on the notion of game reduction. The key idea of a game reduction is to reduce the problem of computing a solution for a given game to the problem of computing a solution for a new game which has an extended game graph but a simpler winning condition. The new game graph contains the memory to solve the original game. Our algorithm computes an equivalence relation on the vertices of the extended game graph and from that deduces equivalent memory contents. We apply our algorithm to Request-Response and Staiger-Wagner games where in both cases we obtain a running time polynomial in the size of the extended game graph. We compare our method to the technique of minimising strategy automata and present an example for which our approach yields a substantially better result.