A pseudo-quasi-polynomial algorithm for mean-payoff parity games

Daviaud, Laure; Jurdziński, Martin; Lazić, Ranko

doi:10.1145/3209108.3209162

Cited by 21 publications

(35 citation statements)

References 25 publications

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“…This allows to simulate a parity game on an alternating Turing machine that uses poly-logarithmic space, which leads to a deterministic algorithm that uses quasipolynomial time and space. This new result has already inspired follow-up works [10,18,23,31,37]. However, benchmarks in the literature have demonstrated that both on random games and real examples the quasi-polynomial is not the best performing one.…”

Section: Introductionmentioning

confidence: 81%

Improving parity games in practice

Stasio

Murano

Prignano

et al. 2021

Ann Math Artif Intell

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Parity games are infinite-round two-player games played on directed graphs whose nodes are labeled with priorities. The winner of a play is determined by the smallest priority (even or odd) that is encountered infinitely often along the play. In the last two decades, several algorithms for solving parity games have been proposed and implemented in , a platform written in OCaml. includes the Zielonka’s recursive algorithm (, for short) which is known to be the best performing one over random games. Notably, several attempts have been carried out with the aim of improving the performance of in , but with small advances in practice. In this work, we deeply revisit the implementation of by dealing with the use of specific data structures and programming languages such as Scala, Java, C++, and Go. Our empirical evaluation shows that these choices are successful, gaining up to three orders of magnitude in running time over the classic version of the algorithm implemented in .

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Section: Introductionmentioning

confidence: 81%

Improving parity games in practice

Stasio

Murano

Prignano

et al. 2021

Ann Math Artif Intell

View full text Add to dashboard Cite

show abstract

“…In particular the last algorithm is of interest as an additional candidate for generalization to nested fixpoints, due to the known good performance of Zielonka's algorithm in practice. Daviaud et al [15] generalize quasipolynomial-time parity game solving by providing a pseudoquasipolynomial algorithm for mean-payoff parity games. On the other hand, Czerwinski et al [14] give a quasipolynomial lower bound on universal trees, implying a barrier for prospective polynomial-time parity game solving algorithms.…”

Section: Related Workmentioning

confidence: 99%

Quasipolynomial Computation of Nested Fixpoints

Hausmann

Schröder

2021

Tools and Algorithms for the Construction and Analysis of Systems

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It is well-known that the winning region of a parity game with n nodes and k priorities can be computed as a k-nested fixpoint of a suitable function; straightforward computation of this nested fixpoint requires $$\mathcal {O}(n^{\frac{k}{2}})$$ O ( n k 2 ) iterations of the function. Calude et al.’s recent quasipolynomial-time parity game solving algorithm essentially shows how to compute the same fixpoint in only quasipolynomially many iterations by reducing parity games to quasipolynomially sized safety games. Universal graphs have been used to modularize this transformation of parity games to equivalent safety games that are obtained by combining the original game with a universal graph. We show that this approach naturally generalizes to the computation of solutions of systems of any fixpoint equations over finite lattices; hence, the solution of fixpoint equation systems can be computed by quasipolynomially many iterations of the equations. We present applications to modal fixpoint logics and games beyond relational semantics. For instance, the model checking problems for the energy $$\mu $$ μ -calculus, finite latticed $$\mu $$ μ -calculi, and the graded and the (two-valued) probabilistic $$\mu $$ μ -calculus – with numbers coded in binary – can be solved via nested fixpoints of functions that differ substantially from the function for parity games but still can be computed in quasipolynomial time; our result hence implies that model checking for these $$\mu $$ μ -calculi is in $$\textsc {QP}$$ QP . Moreover, we improve the exponent in known exponential bounds on satisfiability checking.

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“…In particular the last algorithm is of interest as an additional candidate for generalization to nested fixpoints, due to the known good performance of Zielonka's algorithm in practice. Daviaud et al [19] generalize quasipolynomial-time parity game solving by providing a pseudoquasipolynomial algorithm for mean-payoff parity games. On the other hand, Czerwinski et al [17] give a quasipolynomial lower bound on universal trees, implying a barrier for prospective polynomial-time parity game solving algorithms.…”

Section: Related Workmentioning

confidence: 99%

Quasipolynomial Computation of Nested Fixpoints

Hausmann¹,

Schröder²

2021

Preprint

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It is well-known that the winning region of a parity game with n nodes and k priorities can be computed as a k-nested fixpoint of a suitable function; straightforward computation of this nested fixpoint requires O(n k 2 ) iterations of the function. Calude et al.'s recent quasipolynomial-time parity game solving algorithm essentially shows how to compute the same fixpoint in only quasipolynomially many iterations by reducing parity games to quasipolynomially sized safety games. Universal graphs have been used to modularize this transformation of parity games to equivalent safety games that are obtained by combining the original game with a universal graph. We show that this approach naturally generalizes to the computation of solutions of systems of any fixpoint equations over finite lattices; hence, the solution of fixpoint equation systems can be computed by quasipolynomially many iterations of the equations. We present applications to modal fixpoint logics and games beyond relational semantics. For instance, the model checking problems for the energy µ-calculus, finite latticed µ-calculi, and the graded and the (two-valued) probabilistic µ-calculus -with numbers coded in binary -can be solved via nested fixpoints of functions that differ substantially from the function for parity games but still can be computed in quasipolynomial time; our result hence implies that model checking for these µ-calculi is in QP. Moreover, we improve the exponent in known exponential bounds on satisfiability checking.

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A pseudo-quasi-polynomial algorithm for mean-payoff parity games

Cited by 21 publications

References 25 publications

Improving parity games in practice

Improving parity games in practice

Quasipolynomial Computation of Nested Fixpoints

Quasipolynomial Computation of Nested Fixpoints

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