Generalized Parity Games

  title={Generalized Parity Games},
  author={Krishnendu Chatterjee and Thomas A. Henzinger and Nir Piterman},
  booktitle={Foundations of Software Science and Computation Structure},
We consider games where the winning conditions are disjunctions (or dually, conjunctions) of parity conditions; we call them generalized parity games. These winning conditions, while ω-regular, arise naturally when considering fair simulation between parity automata, secure equilibria for parity conditions, and determinization of Rabin automata. We show that these games retain the computational complexity of Rabin and Streett conditions; i.e., they are NP-complete and co-NP-complete… 

Stochastic o-regular games

It is shown how the notion of secure equilibrium extends the assume-guarantee style of reasoning in the game theoretic framework, and the existence of unique maximal secure equilibrium payoff profiles in turn-based deterministic games is proved.

Combinations of Qualitative Winning for Stochastic Parity Games

A complete picture for the study of combinations of qualitative winning criteria for parity conditions in MDPs and turn-based stochastic games is presented.

Two-Player Boundedness Counter Games

This work considers two-player zero-sum games with winning objectives beyond regular languages, expressed as a parity condition in conjunction with a Boolean combination of boundedness conditions on a finite set of counters, and proves that they are in solvable in NP ∩ CoNP and in PTime if the parity condition is fixed.

Window Parity Games: An Alternative Approach Toward Parity Games with Time Bounds (Full Version)

This work considers two approaches toward inclusion of time bounds in parity games, based on the notion of finitary parity games and parity games with costs and extends both approaches to the multi-dimension setting.

Deciding parity games in quasipolynomial time

It is shown that the parity game can be solved in quasipolynomial time and it is proven that coloured Muller games with n nodes and m colours can be decided in time O((mm · n)5); it is also shown that this bound cannot be improved to O((2m · n), for any c, unless FPT = W[1].

On the Complexity of SPEs in Parity Games

The techniques are based on a recent characterization of SPEs in prefix-independent games that is grounded on the notions of requirements and negotiation, and according to which the plays supported by SPEs are exactly the plays consistent with the requirement that is the least fixed point of the negotiation function.

Doomsday Equilibria for Omega-Regular Games

A new notion of equilibria is proposed, called doomsdayEquilibria, which is a strategy profile such that all players satisfy their own objective, and if any coalition of players deviates and violates even one of the players objective, then the objective of every player is violated.

Constrained existence problem for weak subgame perfect equilibria with omega-regular Boolean objectives

This work focuses on the recent notion of weak subgame perfect equilibrium (weak SPE), a refinement of SPE, and shows that the constrained existence problem for weak SPEs is fixed parameter tractable and is polynomial when the number of players is fixed.

Languages and strategies: a study of regular infinite games

The fundamental Büchi-Landweber Theorem is extended and refine to subclasses of the class of regular languages, in particular the authors consider hierarchies below the starfree languages and distinguish between weak games and strong games.

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

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.



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.

How much memory is needed to win infinite games?

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.

Faster Solutions of Rabin and Streett Games

  • N. PitermanA. Pnueli
  • Computer Science
    21st Annual IEEE Symposium on Logic in Computer Science (LICS'06)
  • 2006
In order to prove completeness of the ranking method, a recursive fixpoint characterization of the winning regions in these games is given and it is shown that by keeping intermediate values during the fixpoint evaluation, such games can be solved symbolically in time O(nk+1k!) and space O( nk-1k!).

Games with secure equilibria

It is proved that in graph games with Borel objectives, which include the games that arise in verification, there may be several Nash equilibria, but there is always a unique maximal payoff profile of secure equilibaria.

On the complexity of omega -automata

  • S. Safra
  • Computer Science
    [Proceedings 1988] 29th Annual Symposium on Foundations of Computer Science
  • 1988
The author presents a determinisation construction that is simpler and yields a single exponent upper bound for the general case, and can be used to obtain an improved complementation construction for Buchi automata that is essentially optimal.

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

The complexity of tree automata and logics of programs

  • E. EmersonC. Jutla
  • Computer Science
    [Proceedings 1988] 29th Annual Symposium on Foundations of Computer Science
  • 1988
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.

From Nondeterministic Buchi and Streett Automata to Deterministic Parity Automata

  • N. Piterman
  • Computer Science
    21st Annual IEEE Symposium on Logic in Computer Science (LICS'06)
  • 2006
This paper shows how to construct deterministic automata with fewer states and, most importantly, parity acceptance conditions and revisits Safra's determinization constructions.

Fair Simulation

The simulation preorder for labeled transition systems is defined locally, and operationally, as a game that relates states with their immediate successor states. Simulation enjoys many appealing

Tree automata, mu-calculus and determinacy

  • E. EmersonC. Jutla
  • 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.