# Strategy Construction in Infinite Ganes with Streett and Rabin Chain Winning Conditions

@inproceedings{Buhrke1996StrategyCI, title={Strategy Construction in Infinite Ganes with Streett and Rabin Chain Winning Conditions}, author={Nils Buhrke and Helmut Lescow and Jens V{\"o}ge}, booktitle={TACAS}, year={1996} }

We consider finite-state games as a model of nonterminating reactive computations. A natural type of specification is given by games with Streett winning condition (corresponding to automata accepting by conjunctions of fairness conditions). We present an algorithm which solves the problem of program synthesis for these specifications. We proceed in two steps: First, we give a reduction of Streett automata to automata with the Rabin chain (or parity) acceptance condition. Secondly, we develop…

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## References

SHOWING 1-10 OF 46 REFERENCES

### Control of Infinite Behavior of Finite Automata

- Computer Science
- 1994

The results represent a direct, efficient and natural solution to Church's problem, the construction of winning strategies for two-player zero-sum $\omega$-regular games of perfect information, and the emptiness problem for automata on infinite trees.

### Solving sequential conditions by finite-state strategies

- Mathematics
- 1969

Our main purpose is to present an algorithm which decides whether or not a condition 𝕮(X, Y) stated in sequential calculus admits a finite automata solution, and produces one if it exists. This…

### Gurevich-Harrington's Games Defined by Finite Automata

- Computer ScienceAnn. Pure Appl. Log.
- 1993

### Trees, automata, and games

- MathematicsSTOC '82
- 1982

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;.

### On the Synthesis of Strategies in Infinite Games

- Computer ScienceSTACS
- 1995

The automata theoretic setting of infinite games (given by “game graphs”), a new construction of winning strategies in finite-state games, and some questions which arise for games over effectively presented infinite graphs are described.

### Automata on Infinite Objects

- Computer ScienceHandbook of Theoretical Computer Science, Volume B: Formal Models and Sematics
- 1990

### Tree automata, mu-calculus and determinacy

- Mathematics, Computer Science[1991] Proceedings 32nd Annual Symposium of Foundations of Computer Science
- 1991

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.

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

- Computer ScienceTheor. Comput. Sci.
- 1995

### Exponential determinization for ω-automata with strong-fairness acceptance condition (extended abstract)

- Computer ScienceSTOC '92
- 1992

The results imply that Streett automata can be used instead of Bu¨chi automata (with the weaker acceptance condition) without any loss of efficiency, and show an exponential determinization construction for any Streett Automaton.

### Propositional Dynamic Logic of looping and converse

- PhilosophySTOC '81
- 1981

Propositional Dynamic Logic can be extended to include both an infinitary iteration construct delta and a backtracking construct converse. The resulting logic does not satisfy the finite model…