# Infinite Games on Finitely Coloured Graphs with Applications to Automata on Infinite Trees

@article{Zielonka1998InfiniteGO, title={Infinite Games on Finitely Coloured Graphs with Applications to Automata on Infinite Trees}, author={Wieslaw Zielonka}, journal={Theor. Comput. Sci.}, year={1998}, volume={200}, pages={135-183} }

## 501 Citations

Complexity Bounds for Regular Games

- Computer Science, MathematicsMFCS
- 2005

A framework in which the expressiveness and succinctness of different types of winning conditions can be compared is established and PSPACE-completeness is established for Emerson-Lei games and for games described by Zielonka DAGs.

Optimizing Winning Strategies in Regular Infinite Games

- Computer ScienceSOFSEM
- 2008

Two criteria for optimization are discussed: memory size of finite automata that execute winning strategies, and - for games with liveness requests as winning conditions - "waiting times" for the satisfaction of requests.

Complexity Bounds for Muller Games

- Computer Science, Mathematics
- 2011

This work establishes a framework in which the expressiveness and succinctness of different types of winning conditions can be compared and shows co-NP-completeness for two classes of union-closed games: games specified by a basis and superset Muller games.

Complexity Bounds for Regular Games (Extended Abstract)

- Computer Science, Mathematics
- 2005

A framework in which the expressiveness and succinctness of different types of winning conditions can be compared is established and PSPACE-completeness is established for Emerson-Lei games and for games described by Zielonka DAGs.

Admissible Strategies in Infinite Games over Graphs

- MathematicsMFCS
- 2009

This work considers games played on finite graphs, whose objective is to obtain a trace belonging to a given set of accepting traces, and provides a characterization of the goals admitting positional admissible strategies and proves the equivalence between the existence of positional winning strategies and the exist of positional subgame perfect strategies.

How much memory is needed to win infinite games?

- Computer ScienceProceedings of Twelfth Annual IEEE Symposium on Logic in Computer Science
- 1997

This work provides matching upper and lower bounds for the size of memory needed by winning strategies in games with a fixed winning condition and proposes a more succinct way of representing winning strategies by means of parallel compositions of transition systems.

Note on winning positions on pushdown games with [omega]-regular conditions

- MathematicsInf. Process. Lett.
- 2003

Pushdown Games with Unboundedness and Regular Conditions

- MathematicsFSTTCS
- 2003

It is shown that the problem of deciding a winner in infinitary two-player perfect information games defined over graphs of configurations of a pushdown automaton is EXPTIME-complete.

Note on winning positions on pushdown games with omega-regular winning conditions

- Mathematics
- 2017

We consider infinite two-player games on pushdown graphs. For parity winning conditions, we show that the set of winning positions of each player is regular and we give an effective construction of…

Complexity Bounds for Muller Games 1

- Computer Science
- 2008

A framework in which the expressiveness and succinctness of different types of winning conditions can be compared is established, and the problem of deciding the winner in Muller games is Pspace-complete, which is used to establish Pspacecompleteness for Emerson-Lei games and for games described by Zielonka DAGs.

## References

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How much memory is needed to win infinite games?

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This work provides matching upper and lower bounds for the size of memory needed by winning strategies in games with a fixed winning condition and proposes a more succinct way of representing winning strategies by means of parallel compositions of transition systems.

On Polynomial-Size Programs Winning Finite-State Games

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It is shown that for two classes of games with Muller winning condition polynomials are both an upper and a lower bound for the size of winning reactive programs.

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This work gives here an alternative and transparent proof of Rabin's result on tree automata, which is based on ideas of his predecessors and especially those of B- and-uuml;chi-&-mdash;.

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It is shown that for tree automata with m states and n pairs nonemptiness can be tested in time O((mn)/sup 3n/), even though the problem is in general NP-complete, and it follows that satisfiability for propositional dynamic logic with a repetition construct and for the propositional mu-calculus can be tests in deterministic single exponential time.

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It is shown that the propositional mu-calculus is equivalent in expressive power to finite automata on infinite trees, which provides a radically simplified, alternative proof of M.O. Rabin's (1989) complementation lemma for tree automata, which is the heart of one of the deepest decidability results.

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Introduction. In this paper we solve the decision problem of a certain secondorder mathematical theory and apply it to obtain a large number of decidability results. The method of solution involves…

Fixpoints for Rabin Tree Automata Make Complementation Easy

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Direct fixpoint constructions for Rabin-automata are described, allowing us to translate modal mu-calculus inductively to Rabin, and provide a new proof of the expressive equivalence of the two formalisms.

Simulating Alternating Tree Automata by Nondeterministic Automata: New Results and New Proofs of the Theorems of Rabin, McNaughton and Safra

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