1,031 research outputs found
The Rabin index of parity games
We study the descriptive complexity of parity games by taking into account
the coloring of their game graphs whilst ignoring their ownership structure.
Colored game graphs are identified if they determine the same winning regions
and strategies, for all ownership structures of nodes. The Rabin index of a
parity game is the minimum of the maximal color taken over all equivalent
coloring functions. We show that deciding whether the Rabin index is at least k
is in PTIME for k=1 but NP-hard for all fixed k > 1. We present an EXPTIME
algorithm that computes the Rabin index by simplifying its input coloring
function. When replacing simple cycle with cycle detection in that algorithm,
its output over-approximates the Rabin index in polynomial time. Experimental
results show that this approximation yields good values in practice.Comment: In Proceedings GandALF 2013, arXiv:1307.416
Synthesising Strategy Improvement and Recursive Algorithms for Solving 2.5 Player Parity Games
2.5 player parity games combine the challenges posed by 2.5 player
reachability games and the qualitative analysis of parity games. These two
types of problems are best approached with different types of algorithms:
strategy improvement algorithms for 2.5 player reachability games and recursive
algorithms for the qualitative analysis of parity games. We present a method
that - in contrast to existing techniques - tackles both aspects with the best
suited approach and works exclusively on the 2.5 player game itself. The
resulting technique is powerful enough to handle games with several million
states
A Delayed Promotion Policy for Parity Games
Parity games are two-player infinite-duration games on graphs that play a
crucial role in various fields of theoretical computer science. Finding
efficient algorithms to solve these games in practice is widely acknowledged as
a core problem in formal verification, as it leads to efficient solutions of
the model-checking and satisfiability problems of expressive temporal logics,
e.g., the modal muCalculus. Their solution can be reduced to the problem of
identifying sets of positions of the game, called dominions, in each of which a
player can force a win by remaining in the set forever. Recently, a novel
technique to compute dominions, called priority promotion, has been proposed,
which is based on the notions of quasi dominion, a relaxed form of dominion,
and dominion space. The underlying framework is general enough to accommodate
different instantiations of the solution procedure, whose correctness is
ensured by the nature of the space itself. In this paper we propose a new such
instantiation, called delayed promotion, that tries to reduce the possible
exponential behaviours exhibited by the original method in the worst case. The
resulting procedure not only often outperforms the original priority promotion
approach, but so far no exponential worst case is known.Comment: In Proceedings GandALF 2016, arXiv:1609.0364
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