## 366 Citations

Measuring Permissiveness in Parity Games: Mean-Payoff Parity Games Revisited

- Computer Science, EconomicsATVA
- 2011

It is proved that deciding (the permissiveness of) a most permissive winning strategy is in NP ∩ coNP, which provides a new study of mean-payoff parity games and gives a new algorithm for solving these games, which beats all previously known algorithms for this problem.

A Linear Time Special Case for MC Games

- MathematicsFundam. Informaticae
- 2002

It is shown 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.

Small Progress Measures for Solving Parity Games

- Computer ScienceSTACS
- 2000

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.

Winning Cores in Parity Games

- Computer Science, Economics2016 31st Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)
- 2016

It is shown that the winning core and the winning region for a player in a parity game are equivalently empty, and a deterministic polynomial-time under-approximation algorithm for solving parity games based on winning core approximation is developed.

Parity Games of Bounded Tree- and Clique-Width

- Computer ScienceFoSSaCS
- 2015

It is shown that deciding the winner of a parity game is in LogCFL, if the underlying graph has bounded tree-width, and in LogDCFL, and it is proven that parity games of bounded clique-width can be solved in logCFL via a log-space reduction to the bounded tree's width case.

The priority promotion approach to parity games

- Computer Science
- 2017

A new family of algorithms is presented, based on the idea of promoting vertices to higher priorities during the search for winning regions, for the solution of parity games, exhibiting the best space complexity among the currently known solutions.

Reduction of stochastic parity to stochastic mean-payoff games

- EconomicsInf. Process. Lett.
- 2008

Solving Mean-Payoff Games via Quasi Dominions

- Computer ScienceTACAS
- 2020

A novel algorithm is proposed for the solution of mean-payoff games that merges together two seemingly unrelated concepts introduced in the context of parity games, small progress measures and quasi dominions and significantly speeds up convergence to the problem solution.

Solving Parity Games Using an Automata-Based Algorithm

- Computer ScienceCIAA
- 2016

Parity games are abstract infinite-round games that take an important role in formal verification and are implemented in a platform named PGSolver, which enabled an empirical evaluation of these algorithms and a better understanding of their relative merits.

Stuttering Equivalence for Parity Games

- LinguisticsArXiv
- 2011

It is demonstrated that stuttering equivalent vertices have the same winner in the parity game, which means that solving a parity game can be accelerated by minimising the game graph with respect to stuttering equivalence.

## References

SHOWING 1-10 OF 19 REFERENCES

The Complexity of Mean Payoff Games

- Computer ScienceCOCOON
- 1995

A pseudopolynomial time algorithm for the solution of mean payoff games, a family of perfect information games introduced by Ehrenfeucht and Mycielski, the decision problem for which is in NP ∩ co-NP.

The Complexity of Mean Payoff Games on Graphs

- MathematicsTheor. Comput. Sci.
- 1995

Pushdown Processes: Games and Model-Checking

- Computer ScienceInf. Comput.
- 1996

It is shown that the model checking problem for push-down automata and the propositional μ-calculus is DEXPTIME-complete and there is a winning strategy which is realized by a pushdown process.

Positional strategies for mean payoff games

- Economics
- 1979

We study some games of perfect information in which two players move alternately along the edges of a finite directed graph with weights attached to its edges. One of them wants to maximize and the…

Tree Automata, Mu-Calculus and Determinacy (Extended Abstract)

- Mathematics, Computer ScienceFOCS 1991
- 1991

The propositional Mu-Calculus is equivalent in expressive power to finite automata on infinite trees and provides a radically simplified, alternative proof of Rabin's 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 ScienceCAV
- 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.

Tree Automata

- LinguisticsArXiv
- 1984

A context-free grammar over the terminal alphabet generating the Dyck language of well-bracketed strings and a product construction for nondeterministic bu-ta A 1 and A 2, to discuss whether there are simpler means of specifying them formally.

Theory of hybrid systems and discrete event systems

- 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.