Justifications and a Reconstruction of Parity Game Solving Algorithms

Parity games are infinite two-player games played on directed graphs. Parity game solvers are used in the domain of formal verification. This paper defines parametrized parity games and introduces an operation, Justify, that determines a winning strategy for a single node. By carefully ordering Justify steps, we reconstruct three algorithms well known from the literature.

[1]  Thomas Wilke,et al.  Automata logics, and infinite games: a guide to current research , 2002 .

[2]  Maurice Bruynooghe,et al.  Improving Parity Game Solvers with Justifications , 2020, VMCAI.

[3]  Jaco van de Pol,et al.  Efficient Instantiation of Parameterised Boolean Equation Systems to Parity Games , 2012, GRAPHITE.

[4]  Erik P. de Vink,et al.  An Overview of the mCRL2 Toolset and Its Recent Advances , 2013, TACAS.

[5]  Michael Luttenberger,et al.  Strix: Explicit Reactive Synthesis Strikes Back! , 2018, CAV.

[6]  S. Safra,et al.  On the complexity of omega -automata , 1988, [Proceedings 1988] 29th Annual Symposium on Foundations of Computer Science.

[7]  Pierre Wolper,et al.  An Automata-Theoretic Approach to Automatic Program Verification (Preliminary Report) , 1986, LICS.

[8]  Marcin Jurdzinski,et al.  Small Progress Measures for Solving Parity Games , 2000, STACS.

[9]  Pawel Parys,et al.  Parity Games: Zielonka's Algorithm in Quasi-Polynomial Time , 2019, MFCS.

[10]  Cristian S. Calude,et al.  Deciding parity games in quasipolynomial time , 2017, STOC.

[11]  Nir Piterman,et al.  From Nondeterministic Buchi and Streett Automata to Deterministic Parity Automata , 2006, 21st Annual IEEE Symposium on Logic in Computer Science (LICS'06).

[12]  E. Emerson,et al.  Tree Automata, Mu-Calculus and Determinacy (Extended Abstract) , 1991, FOCS 1991.

[13]  Ping Hou,et al.  FO(FD): Extending classical logic with rule-based fixpoint definitions , 2010, Theory and Practice of Logic Programming.

[14]  Wieslaw Zielonka,et al.  Infinite Games on Finitely Coloured Graphs with Applications to Automata on Infinite Trees , 1998, Theor. Comput. Sci..

[15]  Sven Schewe,et al.  An Optimal Strategy Improvement Algorithm for Solving Parity and Payoff Games , 2008, CSL.

[16]  Bernd Finkbeiner,et al.  The 5th Reactive Synthesis Competition (SYNTCOMP 2018): Benchmarks, Participants & Results , 2019, ArXiv.

[17]  Tom van Dijk,et al.  Simple Fixpoint Iteration To Solve Parity Games , 2019, GandALF.

[18]  Igor Walukiewicz,et al.  Monadic Second Order Logic on Tree-Like Structures , 1996, STACS.

[19]  Tom van Dijk.  Attracting Tangles to Solve Parity Games , 2018, CAV.

[20]  Pierre Wolper,et al.  An Automata-Theoretic Approach to Branching-Time Model Checking (Extended Abstract) , 1994, CAV.

[21]  Zohar Manna,et al.  A Decision Algorithm for Full Propositional Temporal Logic , 1993, CAV.

[22]  Michael Luttenberger,et al.  Practical synthesis of reactive systems from LTL specifications via parity games , 2019, Acta Informatica.

[23]  Massimo Benerecetti,et al.  Solving Parity Games via Priority Promotion , 2016, CAV.

[24]  Massimo Benerecetti,et al.  A Delayed Promotion Policy for Parity Games , 2016, GandALF.

[25]  Martin Lange,et al.  The Fixpoint-Iteration Algorithm for Parity Games , 2014, GandALF.

[26]  Jan Friso Groote,et al.  A linear translation from CTL* to the first-order modal μ -calculus , 2011, Theor. Comput. Sci..

[27]  Tiziana Margaria,et al.  Tools and algorithms for the construction and analysis of systems: a special issue for TACAS 2017 , 2001, International Journal on Software Tools for Technology Transfer.

[28]  Sanjay Jain,et al.  An ordered approach to solving parity games in quasi polynomial time and quasi linear space , 2017, SPIN.

[29]  Massimo Benerecetti,et al.  Improving Priority Promotion for Parity Games , 2016, Haifa Verification Conference.

[30]  Sven Schewe,et al.  CTL* synthesis via LTL synthesis , 2017, SYNT@CAV.