Tree automata, Mu-Calculus and determinacy
SFCS '91 Proceedings of the 32nd annual symposium on Foundations of computer science
Languages, automata, and logic
Handbook of formal languages, vol. 3
Infinite games on finitely coloured graphs with applications to automata on infinite trees
Theoretical Computer Science
Deciding the winner in parity games is in UP ∩ co-UP
Information Processing Letters
Graph Algorithms
Data Structures and Algorithms
Data Structures and Algorithms
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
Combinatorial Algorithms: Theory and Practice
Combinatorial Algorithms: Theory and Practice
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MC games are infinite duration two-player games played on graphs. Deciding the winner in MC games is equivalent to the the modal mu-calculus model checking. In this article we provide a linear time algorithm for a class of MC games. We show that, if all cycles in each strongly connected component of the game graph have at least one common vertex, the winner can be found in linear time. Our results hold also for parity games, which are equivalent to MC games.