DAG-Width and Parity Games

Berwanger, Dietmar; Dawar, Anuj; Hunter, Paul; Kreutzer, Stephan

doi:10.1007/11672142_43

Cited by 93 publications

(100 citation statements)

References 17 publications

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“…In particular, modal and alternating-time µ-calculus model checking [5,4], synthesis [10,9] and satisfiability checking [5,1,7,8] for reactive systems, module checking [6], and ATL* model checking [3,4] can be reduced to solving parity games. This relevance of parity games led to a serial of different approaches to solving them [11][12][13][14][15][16][17][18][19][20][21][22][23][24][25].…”

Section: Introductionmentioning

confidence: 99%

Solving parity games in big steps

Schewe

2017

Journal of Computer and System Sciences

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Abstract. This paper proposes a new algorithm that improves the complexity bound for solving parity games. Our approach combines McNaughton's iterated fixed point algorithm with a preprocessing step, which is called prior to every recursive call. The preprocessing uses ranking functions similar to Jurdziński's, but with a restricted codomain, to determine all winning regions smaller than a predefined parameter. The combination of the preprocessing step with the recursive call guarantees that McNaughton's algorithm proceeds in big steps, whose size is bounded from below by the chosen parameter. Higher parameters guarantee small call trees, but to the cost of an expensive preprocessing step. An optimal parameter balance the cost of the recursive call and the preprocessing step, resulting in an O(m n γ(c) ) complexity bound for solving parity games with c colors, n positions and m edges, where2 ⌋ if c is even, and γ(c)= c 3 + 1 2 − 1 ⌈ c 2 ⌉⌊ c 2 ⌋ if c is odd.

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Section: Introductionmentioning

confidence: 99%

Solving parity games in big steps

Schewe

2017

Journal of Computer and System Sciences

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“…[11,8,10,9]), restriction of parity games to classes for which polynomialtime algorithms can be devised as complete solvers (e.g. [1,3]), and practical improvements to solvers so that they perform well across benchmarks (e.g. [5]).…”

Section: Introductionmentioning

confidence: 99%

Fatal Attractors in Parity Games

Huth

Kuo

Piterman

2013

Lecture Notes in Computer Science

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Abstract. We study a new form of attractor in parity games and use it to define solvers that run in PTIME and are partial in that they do not solve all games completely. Technically, for color c this new attractor determines whether player c%2 can reach a set of nodes X of color c whilst avoiding any nodes of color less than c. Such an attractor is fatal if player c%2 can attract all nodes in X back to X in this manner. Our partial solvers detect fixed-points of nodes based on fatal attractors and correctly classify such nodes as won by player c%2. Experimental results show that our partial solvers completely solve benchmarks that were constructed to challenge existing full solvers. Our partial solvers also have encouraging run times in practice. For one partial solver we prove that its runtime is in O(| V | 3 ), that its output game is independent of the order in which attractors are computed, and that it solves all Büchi games.

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“…More efficient algorithms for solving parity games will therefore foster the development of performant model checkers and contribute to bringing synthesis techniques to practice. The quest for performant algorithms [1,[10][11][12][13][14][15][16][17][18][19][20][21][22][23][24][25] for solving them has therefore been an active field of research during the last decades.…”

Section: Introductionmentioning

confidence: 99%

An Optimal Strategy Improvement Algorithm for Solving Parity and Payoff Games

Schewe

2008

Lecture Notes in Computer Science

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Abstract. This paper presents a novel strategy improvement algorithm for parity and payoff games, which is guaranteed to select, in each improvement step, an optimal combination of local strategy modifications. Current strategy improvement methods stepwise improve the strategy of one player with respect to some ranking function, using an algorithm with two distinct phases: They first choose a modification to the strategy of one player from a list of locally profitable changes, and subsequently evaluate the modified strategy. This separation is unfortunate, because current strategy improvement algorithms have no effective means to predict the global effect of the individual local modifications beyond classifying them as profitable, adversarial, or stale. Furthermore, they are completely blind towards the cross effect of different modifications: Applying one profitable modification may render all other profitable modifications adversarial. Our new construction overcomes the traditional separation between choosing and evaluating the modification to the strategy. It thus improves over current strategy improvement algorithms by providing the optimal improvement in every step, selecting the best combination of local updates from a superset of all profitable and stale changes.

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DAG-Width and Parity Games

Cited by 93 publications

References 17 publications

Solving parity games in big steps

Solving parity games in big steps

Fatal Attractors in Parity Games

An Optimal Strategy Improvement Algorithm for Solving Parity and Payoff Games

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