Tree automata, Mu-Calculus and determinacy
SFCS '91 Proceedings of the 32nd annual symposium on Foundations of computer science
Languages, automata, and logic
Handbook of formal languages, vol. 3
Infinite games on finitely coloured graphs with applications to automata on infinite trees
Theoretical Computer Science
Antichain-Based Universality and Inclusion Testing over Nondeterministic Finite Tree Automata
CIAA '08 Proceedings of the 13th international conference on Implementation and Applications of Automata
Alpaga: A Tool for Solving Parity Games with Imperfect Information
TACAS '09 Proceedings of the 15th International Conference on Tools and Algorithms for the Construction and Analysis of Systems: Held as Part of the Joint European Conferences on Theory and Practice of Software, ETAPS 2009,
ICALP'03 Proceedings of the 30th international conference on Automata, languages and programming
TACAS'07 Proceedings of the 13th international conference on Tools and algorithms for the construction and analysis of systems
Antichains: alternative algorithms for LTL satisfiability and model-checking
TACAS'08/ETAPS'08 Proceedings of the Theory and practice of software, 14th international conference on Tools and algorithms for the construction and analysis of systems
A lattice theory for solving games of imperfect information
HSCC'06 Proceedings of the 9th international conference on Hybrid Systems: computation and control
Antichains: a new algorithm for checking universality of finite automata
CAV'06 Proceedings of the 18th international conference on Computer Aided Verification
CAV'05 Proceedings of the 17th international conference on Computer Aided Verification
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We consider two-player parity games with imperfect information in which strategies rely on observations that provide imperfect information about the history of a play. To solve such games, i.e., to determine the winning regions of players and corresponding winning strategies, one can use the subset construction to build an equivalent perfect-information game. Recently, an algorithm that avoids the inefficient subset construction has been proposed. The algorithm performs a fixed-point computation in a lattice of antichains, thus maintaining a succinct representation of state sets. However, this representation does not allow to recover winning strategies. In this paper, we build on the antichain approach to develop an algorithm for constructing the winning strategies in parity games of imperfect information. One major obstacle in adapting the classical procedure is that the complementation of attractor sets would break the invariant of downward-closedness on which the antichain representation relies. We overcome this difficulty by decomposing problem instances recursively into games with a combination of reachability, safety, and simpler parity conditions. We also report on an experimental implementation of our algorithm; to our knowledge, this is the first implementation of a procedure for solving imperfect-information parity games on graphs.