Solving μ-Calculus Parity Games by Symbolic Planning

2009 ◽  
pp. 15-33 ◽  
Author(s):  
Marco Bakera ◽  
Stefan Edelkamp ◽  
Peter Kissmann ◽  
Clemens D. Renner
Keyword(s):  
Parity Games ◽  
Symbolic Planning

scholarly journals Higher-order Recursion Schemes and Collapsible Pushdown Automata: Logical Properties

2021 ◽  
Vol 22 (2) ◽  
pp. 1-37
Author(s):  
Christopher H. Broadbent ◽  
Arnaud Carayol ◽  
C.-H. Luke Ong ◽  
Olivier Serre
Keyword(s):  
Model Checking ◽  
Free Variable ◽  
Higher Order ◽  
Second Order ◽  
Effective Solution ◽  
Parity Games ◽  
Transition Graphs ◽  
Second Order Logic ◽  
Pushdown Automata ◽  
Monadic Second Order Logic

This article studies the logical properties of a very general class of infinite ranked trees, namely, those generated by higher-order recursion schemes. We consider, for both monadic second-order logic and modal -calculus, three main problems: model-checking, logical reflection (a.k.a. global model-checking, that asks for a finite description of the set of elements for which a formula holds), and selection (that asks, if exists, for some finite description of a set of elements for which an MSO formula with a second-order free variable holds). For each of these problems, we provide an effective solution. This is obtained, thanks to a known connection between higher-order recursion schemes and collapsible pushdown automata and on previous work regarding parity games played on transition graphs of collapsible pushdown automata.

scholarly journals OBLIGATION BLACKWELL GAMES AND P-AUTOMATA

2017 ◽  
Vol 82 (2) ◽  
pp. 420-452
Author(s):  
KRISHNENDU CHATTERJEE ◽  
NIR PITERMAN
Keyword(s):  
Markov Chains ◽  
Decision Problem ◽  
Value Function ◽  
Acceptance Condition ◽  
Parity Games ◽  
The Value Function

AbstractWe generalize winning conditions in two-player games by adding a structural acceptance condition called obligations. Obligations are orthogonal to the linear winning conditions that define whether a play is winning. Obligations are a declaration that player 0 can achieve a certain value from a configuration. If the obligation is met, the value of that configuration for player 0 is 1.We define the value in such games and show that obligation games are determined. For Markov chains with Borel objectives and obligations, and finite turn-based stochastic parity games with obligations we give an alternative and simpler characterization of the value function. Based on this simpler definition we show that the decision problem of winning finite turn-based stochastic parity games with obligations is in NP∩co-NP. We also show that obligation games provide a game framework for reasoning about p-automata.

scholarly journals Stochastic Parity Games on Lossy Channel Systems

2015 ◽  
Vol 10 (4) ◽  
Author(s):  
Parosh Abdulla ◽  
Lorenzo Clemente ◽  
Richard Mayr ◽  
Sven Sandberg
Keyword(s):  
Parity Games ◽  
Lossy Channel ◽  
Channel Systems

scholarly journals A Discrete Stratety Improvement Algorithm for Solving Parity Games

2000 ◽  
Vol 7 (48) ◽  
Author(s):  
Marcin Jurdzinski ◽  
Jens Vöge
Keyword(s):  
Linear Programming ◽  
Conceptual Understanding ◽  
Polynomial Time ◽  
Stochastic Games ◽  
Real Numbers ◽  
Improvement Algorithm ◽  
Winning Strategies ◽  
Parity Games ◽  
Present Algorithm ◽  
Standing Problem

A discrete strategy improvement algorithm is given for constructing<br />winning strategies in parity games, thereby providing<br />also a new solution of the model-checking problem for the modal<br />-calculus. Known strategy improvement algorithms, as proposed<br />for stochastic games by Homan and Karp in 1966, and for discounted payoff games and parity games by Puri in 1995, work with real numbers and require solving linear programming instances involving high precision arithmetic. In the present algorithm for parity games these difficulties are avoided by the use of discrete vertex valuations in which information about the relevance of vertices and certain distances is coded. An efficient implementation is given for a strategy improvement step. Another advantage of the present approach is that it provides a better conceptual understanding and easier analysis of strategy improvement algorithms for parity games. However, so far it is not known whether the present algorithm works in polynomial time. The long standing problem whether parity games can be solved in polynomial time remains open.

scholarly journals Robust Exponential Worst Cases for Divide-et-Impera Algorithms for Parity Games

2017 ◽  
Vol 256 ◽  
pp. 121-135 ◽  
Author(s):  
Massimo Benerecetti ◽  
Daniele Dell'Erba ◽  
Fabio Mogavero
Keyword(s):  
Parity Games

A Simple Algorithm for Solving Qualitative Probabilistic Parity Games

2016 ◽  
pp. 291-311 ◽  
Author(s):  
Ernst Moritz Hahn ◽  
Sven Schewe ◽  
Andrea Turrini ◽  
Lijun Zhang
Keyword(s):  
Simple Algorithm ◽  
Parity Games
Sign in / Sign up

Export Citation Format

Share Document