• Corpus ID: 16830459

Strategy Derivation for Small Progress Measures

  title={Strategy Derivation for Small Progress Measures},
  author={Maciej Gazda and Tim A. C. Willemse},
Small Progress Measures is one of the most efficient parity game solving algorithms. The original algorithm provides the full solution (winning regions and strategies) in $O(dm \cdot (n/ \lceil d/2 \rceil)^{\lceil d/2 \rceil} )$ time, and requires a re-run of the algorithm on one of the winning regions. We provide a novel operational interpretation of progress measures, and modify the algorithm so that it derives the winning strategies for both players in one pass. This reduces the upper bound… 

Figures from this paper

Improvement in Small Progress Measures
The algorithm is modified so that it derives the winning strategy for both players in one pass, which reduces the upper bound on strategy derivation for SPM to O(dm.(n/floor(d/2))^floor( d/2)).
Solving 3-Color Parity Games in O(n2) Time
A new algorithm, based on simple attractor constructions, is presented, showing that 3-color parity games are not harder to solve in general than other polynomial time games.
Improvement in small progress measures
The final author version and the galley proof are versions of the publication after peer review that features the final layout of the paper including the volume, issue and page numbers.


Small Progress Measures for Solving Parity Games
A new algorithm for deciding the winner in parity games, and hence also for the modal µ-calculus model checking, based on a notion of game progress measures, characterized as pre-fixed points of certain monotone operators on a complete lattice.
Solving parity games in big steps
  • S. Schewe
  • Computer Science
    J. Comput. Syst. Sci.
  • 2007
A Discrete Strategy Improvement Algorithm for Solving Parity Games
A discrete strategy improvement algorithm is given for constructing winning strategies in parity games, thereby providing also a new solution of the model-checking problem for the modal μ-calculus.
Algorithms for Parity Games
  • H. Klauck
  • Computer Science
    Automata, Logics, and Infinite Games
  • 2001
The aim of this chapter is to review some of the algorithmic approaches to the problem of computing winning strategies in parity games with finite arenas and other two-player games, and to underline the importance of looking for an efficient algorithm solving this particular problem.
An Optimal Strategy Improvement Algorithm for Solving Parity and Payoff Games
A novel strategy improvement algorithm for parity and payoff games is presented, which is guaranteed to select, in each improvement step, an optimal combination of local strategy modifications.
Non-oblivious Strategy Improvement
A structural property of these games is described, and it is shown that these structures can affect the behaviour of strategy improvement and can be used to accelerate strategy improvement algorithms.
Zielonka's Recursive Algorithm: dull, weak and solitaire games and tighter bounds
It is shown that an optimisation of Zielonka's algorithm permits solving games from all three classes in polynomial time, and that there is a family of (non-special) games M that permits the algorithm to establish a lower bound of 2^(n/3), improving on the previous lower bound for the algorithm.
Solving Parity Games in Practice
A generic solver is presented that intertwines optimisations with any of the existing parity game algorithms which is only called on parts of a game that cannot be solved faster by simpler methods, showing that using this approach vastly speeds up the solving process.
Infinite Games Played on Finite Graphs
Infinite Games on Finitely Coloured Graphs with Applications to Automata on Infinite Trees
  • W. Zielonka
  • Mathematics, Computer Science
    Theor. Comput. Sci.
  • 1998