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}
}
  • W. Zielonka
  • Published 28 June 1998
  • Mathematics, Computer Science
  • Theor. Comput. Sci.

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References

SHOWING 1-10 OF 35 REFERENCES
How much memory is needed to win infinite games?
TLDR
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.
Infinite Games Played on Finite Graphs
On Polynomial-Size Programs Winning Finite-State Games
TLDR
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.
Progress measures, immediate determinacy, and a subset construction for tree automata
  • Nils Klarlund
  • Mathematics
    [1992] Proceedings of the Seventh Annual IEEE Symposium on Logic in Computer Science
  • 1992
TLDR
Using the concept of a progress measure, a simplified proof is given of M.O. Rabin's (1969) fundamental result that the languages defined by tree automata are closed under complementation and a graph-theoretic duality theorem for such acceptance conditions is shown.
Trees, automata, and games
TLDR
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;.
The complexity of tree automata and logics of programs
  • E. Emerson, C. Jutla
  • Computer Science
    [Proceedings 1988] 29th Annual Symposium on Foundations of Computer Science
  • 1988
TLDR
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.
Tree automata, mu-calculus and determinacy
  • E. Emerson, C. Jutla
  • Mathematics, Computer Science
    [1991] Proceedings 32nd Annual Symposium of Foundations of Computer Science
  • 1991
TLDR
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.
Decidability of second-order theories and automata on infinite trees
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
TLDR
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.
...
...