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

Maciej Gazda
Tim A.C. Willemse

Dull, weak and nested solitaire games are important classes of parity games, capturing, among others, alternation-free mu-calculus and ECTL* model checking problems. These classes can be solved in polynomial time using dedicated algorithms. We investigate the complexity of Zielonka's Recursive algorithm for solving these special games, showing that the algorithm runs in O(d (n + m)) on weak games, and, somewhat surprisingly, that it requires exponential time to solve dull games and (nested) solitaire games. For the latter classes, we provide a family of games G, allowing us to establish a lower bound of 2^(n/3). We show that an optimisation of Zielonka's algorithm permits solving games from all three classes in polynomial time. Moreover, we show that there is a family of (non-special) games M that permits us to establish a lower bound of 2^(n/3), improving on the previous lower bound for the algorithm.

In Gabriele Puppis and Tiziano Villa: Proceedings Fourth International Symposium on Games, Automata, Logics and Formal Verification (GandALF 2013), Borca di Cadore, Dolomites, Italy, 29-31th August 2013, Electronic Proceedings in Theoretical Computer Science 119, pp. 7–20.
Published: 16th July 2013.

ArXived at: https://dx.doi.org/10.4204/EPTCS.119.4 bibtex PDF
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