Succinct progress measures for solving parity games

Jurdziński, Marcin; Lazić, Ranko

doi:10.1109/lics.2017.8005092

Cited by 62 publications

(181 citation statements)

References 22 publications

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“…We argue that in the separation approach, it is appropriate to slightly adjust the choice of languages to be separated, from EvenLoops n and OddLoops n proposed by Bojańczyk and Czerwiński [3] to the more suitable EvenCycles n and OddCycles n (see Section 3.1 for the definitions). We also verify, in Section 4, that all the three distinct techniques of solving parity games in quasi-polynomial time considered in the recent literature (play summaries [5,20,16], progress measures [25], and register games [27]) yield separators for languages EvenCycles n and LimsupOdd, which (as we argue in Section 3.2) makes them suitable for the separation approach.…”

Section: Our Contributionsupporting

confidence: 58%

“…The significance of our main technical results is that they provide evidence against the hope that any of the existing technical approaches to developing quasipolynomial algorithms for solving parity games [5,25,16,27] may lead to further improvements to sub-quasipolynomial algorithms. In other words, our quasipolynomial lower bounds for universal trees and separators form a barrier that all existing approaches must overcome in the ongoing quest for a polynomial-time algorithm for solving parity games.…”

Section: Our Contributionmentioning

confidence: 93%

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Universal trees grow inside separating automata: Quasi-polynomial lower bounds for parity games

Czerwiński¹,

Daviaud²,

Fijalkow³

et al. 2019

Proceedings of the Thirtieth Annual ACM-SIAM Symposium on Discrete Algorithms

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Several distinct techniques have been proposed to design quasi-polynomial algorithms for solving parity games since the breakthrough result of Calude, Jain, Khoussainov, Li, and Stephan (2017): play summaries, progress measures and register games. We argue that all those techniques can be viewed as instances of the separation approach to solving parity games, a key technical component of which is constructing (explicitly or implicitly) an automaton that separates languages of words encoding plays that are (decisively) won by either of the two players. Our main technical result is a quasi-polynomial lower bound on the size of such separating automata that nearly matches the current best upper bounds. This forms a barrier that all existing approaches must overcome in the ongoing quest for a polynomial-time algorithm for solving parity games.The key and fundamental concept that we introduce and study is a universal ordered tree. The technical highlights are a quasi-polynomial lower bound on the size of universal ordered trees and a proof that every separating safety automaton has a universal tree hidden in its state space.

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Section: Our Contributionsupporting

confidence: 58%

Section: Our Contributionmentioning

confidence: 93%

Universal trees grow inside separating automata: Quasi-polynomial lower bounds for parity games

Czerwiński¹,

Daviaud²,

Fijalkow³

et al. 2019

Proceedings of the Thirtieth Annual ACM-SIAM Symposium on Discrete Algorithms

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show abstract

“…We believe that the integration approach we devised is general enough to be applied to other types of games. In particular, the application of quasi dominions in conjunction with progress measure based approaches, such as those of [27] and [21], may lead to practically efficient quasi polynomial algorithms for parity games and their quantitative extensions.…”

Section: Discussionmentioning

confidence: 99%

Solving Mean-Payoff Games via Quasi Dominions

Benerecetti

Dell’Erba

Mogavero

2020

Lecture Notes in Computer Science

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We propose a novel algorithm 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. We show that the integration of the two notions can be highly beneficial and significantly speeds up convergence to the problem solution. Experiments show that the resulting algorithm performs orders of magnitude better than the asymptotically-best solution algorithm currently known, without sacrificing on the worst-case complexity.A two-player turn-based arena is a tuple A = Ps ⊕ , Ps ⊟ , Mv , with Ps ⊕ ∩ Ps ⊟ = ∅ and Ps Ps ⊕ ∪ Ps ⊟ , such that Ps, Mv is a finite directed graph without sinks. Ps ⊕ (resp., Ps ⊟ ) is the set of 1. The experiments were carried out on a 64-bit 3.9GHz quad-core machine, with INTEL i5-6600K processor and 8GB of RAM, running UBUNTU 18.04.

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“…While subexponential solving algorithms have been devised, despite the (deceptive) simplicity of the game and a continuous research effort, no polynomial time algorithm for solving parity games has been found. However, only recently the problem was shown to be solvable in quasi-polynomial time [10,22,17].…”

Section: Introductionmentioning

confidence: 99%

“…Algorithms from the SI category directly compute the winning strategies for both players; e.g., by means of policy iteration or by maintaining some statistics about the plays that can emerge from a vertex. The recent quasi-polynomial algorithms [10,22,17] all fall in this category, but also classical algorithms such as Jurdziński's small progress measures algorithm [21], and, to some extent, the Fixpoint-Iteration (FI) algorithm [8], which is closely related to the small progress measures algorithm, see ibid. The DI category of algorithms proceed by (recursively) decomposing the game graph in dominions: small subgraphs that are won by a single player and from which the opponent cannot escape.…”

Section: Introductionmentioning

confidence: 99%

A Comparison of BDD-Based Parity Game Solvers

Sanchez¹,

Wesselink

Willemse

2018

Electron. Proc. Theor. Comput. Sci.

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Parity games are two player games with omega-winning conditions, played on finite graphs. Such games play an important role in verification, satisfiability and synthesis. It is therefore important to identify algorithms that can efficiently deal with large games that arise from such applications. In this paper, we describe our experiments with BDD-based implementations of four parity game solving algorithms, viz. Zielonka's recursive algorithm, the more recent Priority Promotion algorithm, the Fixpoint-Iteration algorithm and the automata based APT algorithm. We compare their performance on several types of random games and on a number of cases taken from the Keiren benchmark set.

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Succinct progress measures for solving parity games

Cited by 62 publications

References 22 publications

Universal trees grow inside separating automata: Quasi-polynomial lower bounds for parity games

Universal trees grow inside separating automata: Quasi-polynomial lower bounds for parity games

Solving Mean-Payoff Games via Quasi Dominions

A Comparison of BDD-Based Parity Game Solvers

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