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A subexponential randomized algorithm for the simple stochastic game problem
Information and Computation
The complexity of mean payoff games on graphs
Theoretical Computer Science
Theory of hybrid systems and discrete event systems
Theory of hybrid systems and discrete event systems
An improved algorithm for the evaluation of fixpoint expressions
Theoretical Computer Science
Infinite games on finitely coloured graphs with applications to automata on infinite trees
Theoretical Computer Science
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Journal of the ACM (JACM)
Reasoning about The Past with Two-Way Automata
ICALP '98 Proceedings of the 25th International Colloquium on Automata, Languages and Programming
Small Progress Measures for Solving Parity Games
STACS '00 Proceedings of the 17th Annual Symposium on Theoretical Aspects of Computer Science
A Discrete Strategy Improvement Algorithm for Solving Parity Games
CAV '00 Proceedings of the 12th International Conference on Computer Aided Verification
On Model-Checking for Fragments of µ-Calculus
CAV '93 Proceedings of the 5th International Conference on Computer Aided Verification
A deterministic subexponential algorithm for solving parity games
SODA '06 Proceedings of the seventeenth annual ACM-SIAM symposium on Discrete algorithm
From Nondeterministic Buchi and Streett Automata to Deterministic Parity Automata
LICS '06 Proceedings of the 21st Annual IEEE Symposium on Logic in Computer Science
A combinatorial strongly subexponential strategy improvement algorithm for mean payoff games
Discrete Applied Mathematics
Synthesis of asynchronous systems
LOPSTR'06 Proceedings of the 16th international conference on Logic-based program synthesis and transformation
COCOON'99 Proceedings of the 5th annual international conference on Computing and combinatorics
Solving parity games in big steps
FSTTCS'07 Proceedings of the 27th international conference on Foundations of software technology and theoretical computer science
STACS'06 Proceedings of the 23rd Annual conference on Theoretical Aspects of Computer Science
Solving Parity Games in Practice
ATVA '09 Proceedings of the 7th International Symposium on Automated Technology for Verification and Analysis
A Solver for Modal Fixpoint Logics
Electronic Notes in Theoretical Computer Science (ENTCS)
Non-oblivious strategy improvement
LPAR'10 Proceedings of the 16th international conference on Logic for programming, artificial intelligence, and reasoning
Verification of reactive systems via instantiation of Parameterised Boolean Equation Systems
Information and Computation
Verification of reactive systems via instantiation of Parameterised Boolean Equation Systems
Information and Computation
Subexponential lower bounds for randomized pivoting rules for the simplex algorithm
Proceedings of the forty-third annual ACM symposium on Theory of computing
A subexponential lower bound for the random facet algorithm for parity games
Proceedings of the twenty-second annual ACM-SIAM symposium on Discrete Algorithms
A superpolynomial lower bound for strategy iteration based on snare memorization
Discrete Applied Mathematics
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This paper presents a novel strategy improvement algorithm for parity and payoff games, which is guaranteed to select, in each improvement step, an optimal combination of local strategy modifications. Current strategy improvement methods stepwise improve the strategy of one player with respect to some ranking function, using an algorithm with two distinct phases: They first choose a modification to the strategy of one player from a list of locallyprofitable changes, and subsequently evaluate the modified strategy. This separation is unfortunate, because current strategy improvement algorithms have no effective means to predict the global effectof the individual local modifications beyond classifying them as profitable, adversarial, or stale. Furthermore, they are completely blind towards the cross effectof different modifications: Applying one profitable modification may render all other profitable modifications adversarial. Our new construction overcomes the traditional separation between choosing and evaluating the modification to the strategy. It thus improves over current strategy improvement algorithms by providing the optimal improvementin every step, selecting the best combination of local updates from a superset of all profitable and stale changes.