Zielonka's Recursive Algorithm: dull, weak and solitaire games and tighter bounds

Gazda, Maciej; Willemse, Tim A. C.

doi:10.4204/eptcs.119.4

Cited by 8 publications

(10 citation statements)

References 18 publications

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“…For instance, the recursive algorithm is regarded as one of the best algorithms in practice, which is corroborated by experiments [7]. However, until our recent work [8] where we showed the algorithm is well-behaved on several important classes of parity games, there was no satisfactory explanation why this would be the case. In a similar vein, in ibid.…”

Section: Introductionmentioning

confidence: 79%

“…As for the future work, we would like to perform an analysis of SPM's behaviour on special classes of games, along the same lines as we have done in case of the recursive algorithm [8]. More specifically, we would like to identify the games for which SPM runs in polynomial time, and study enhancements that allow to solve more types of games efficiently.…”

Section: Discussionmentioning

confidence: 99%

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Improvement in Small Progress Measures

Gazda¹,

Willemse²

2015

Electron. Proc. Theor. Comput. Sci.

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Small Progress Measures is one of the classical parity game solving algorithms. For games with n vertices, m edges and d different priorities, the original algorithm computes the winning regions and a winning strategy for one of the players in O(dm · (n/⌊d/2⌋) ⌊d/2⌋ ) time. Computing a winning strategy for the other player requires a re-run of the algorithm on that player's winning region, thus increasing the runtime complexity to O(dm · (n/⌈d/2⌉) ⌈d/2⌉ ) for computing the winning regions and winning strategies for both players. We modify the algorithm so that it derives the winning strategy for both players in one pass. This reduces the upper bound on strategy derivation for SPM to O(dm · (n/⌊d/2⌋) ⌊d/2⌋ ). At the basis of our modification is a novel operational interpretation of the least progress measure that we provide.

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Section: Introductionmentioning

confidence: 79%

Section: Discussionmentioning

confidence: 99%

Improvement in Small Progress Measures

Gazda¹,

Willemse²

2015

Electron. Proc. Theor. Comput. Sci.

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“…Friedmann et al provided superpolynomial or exponential lower bounds for many of such rules [1,16,17,20,21,22,23], as well as Fearnley and Savani recently [15]. For a long time, the main attractor-based algorithm was the recursive algorithm by McNaughton [32] and Zielonka [34], for which Friedmann also showed an exponential lower bound [19] and later Gazda and Willemse [25] improved upon this lower bound. These lower bounds are resistant against techniques like inflation, compression and SCC decomposition, even when applied to each recursive call.…”

Section: Discussionmentioning

confidence: 99%

A Parity Game Tale of Two Counters

Dijk

2019

Electron. Proc. Theor. Comput. Sci.

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Parity games have important practical applications in formal verification and synthesis, especially for problems related to linear temporal logic and to the modal mu-calculus. The problem is believed to admit a solution in polynomial time, motivating researchers to find candidates for such an algorithm and to defeat these algorithms. We present a parameterized parity game called the Two Counters game, which provides an exponential lower bound for a wide range of parity game solving algorithms. We are the first to provide an exponential lower bound to priority promotion with the delayed promotion policy, and the first to provide such a lower bound to tangle learning.

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“…The algorithm by Zielonka [43] is a recursive solver that despite its relatively bad theoretical complexity is known to outperform other algorithms in practice [19]. Furthermore, tight bounds are known for various classes of games [21]. Zielonka's recursive algorithm is based on attractor computation.…”

Section: Zielonka's Recursive Algorithmmentioning

confidence: 99%

Oink: An Implementation and Evaluation of Modern Parity Game Solvers

Dijk¹

2018

Lecture Notes in Computer Science

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Abstract. Parity games have important practical applications in formal verification and synthesis, especially to solve the model-checking problem of the modal mu-calculus. They are also interesting from the theory perspective, as they are widely believed to admit a polynomial solution, but so far no such algorithm is known. In recent years, a number of new algorithms and improvements to existing algorithms have been proposed. We implement a new and easy to extend tool Oink, which is a high-performance implementation of modern parity game algorithms. We further present a comprehensive empirical evaluation of modern parity game algorithms and solvers, both on real world benchmarks and randomly generated games. Our experiments show that our new tool Oink outperforms the current state-of-the-art.

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Zielonka's Recursive Algorithm: dull, weak and solitaire games and tighter bounds

Cited by 8 publications

References 18 publications

Improvement in Small Progress Measures

Improvement in Small Progress Measures

A Parity Game Tale of Two Counters

Oink: An Implementation and Evaluation of Modern Parity Game Solvers

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