# Implementation of a Strategy Improvement Algorithm for Finite-State Parity Games

@inproceedings{Schmitz2000ImplementationOA,
title={Implementation of a Strategy Improvement Algorithm for Finite-State Parity Games},
author={Dominik Schmitz and Jens V{\"o}ge},
booktitle={CIAA},
year={2000}
}
• Published in CIAA 24 July 2000
• Computer Science
An implementation of a recent algorithm (Voge, Jurdzinski, to appear in CAV 2000) for the construction of winning strategies in infinite games is presented. The games under consideration are "finite-state parity games", i.e. games over finite graphs where the winning condition is inherited from ω-automata with parity acceptance. The emphasis of the paper is the development of a user interface which supports the researcher in case studies for algorithms of ω-automata theory. Examples of such…
10 Citations

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## References

SHOWING 1-8 OF 8 REFERENCES

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

• Computer Science
TACAS
• 1996
An algorithm is presented which solves the problem of program synthesis for finite-state games with Streett winning condition by developing an inductive strategy construction over Rabin chain automata which yields finite automata that realize winning strategies.

### 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.

### On Model-Checking for Fragments of µ-Calculus

• Computer Science
CAV
• 1993
It is shown that the logic L2 is as expressive as ECTL* given in [13], and the model checking problem for the μ-calculus is equivalent to the non-emptiness problem of parity tree automata.

### Theory of hybrid systems and discrete event systems

• A. Puri
• Mathematics, Computer Science
• 1996
It is shown that for hybrid automata with rectangular inclusions, the reachability question can be answered in a finite number of steps and that an $\omega$-automata game with the chain acceptance condition can be solved as a mean payoff game.

### Languages, Automata, and Logic

• W. Thomas
• Computer Science
Handbook of Formal Languages
• 1997
The subject of this chapter is the study of formal languages (mostly languages recognizable by finite automata) in the framework of mathematical logic.

### A Discrete Strategy Improvement Algorithm for Solving Parity Games

• Computer Science
CAV
• 2000
A discrete strategy improvement algorithm is given for constructing winning strategies in parity games, thereby providing also a new solution of the model-checking problem for the modal μ-calculus.

### Small Progress Measures for Solving Parity Games

A new algorithm for deciding the winner in parity games, and hence also for the modal µ-calculus model checking, based on a notion of game progress measures, characterized as pre-fixed points of certain monotone operators on a complete lattice.