Combinatorial structure and randomized subexponential algorithms for infinite games

Henrik Björklund, Sergei Vorobyov
2005 Theoretical Computer Science  
The complexity of solving infinite games, including parity, mean payoff, and simple stochastic, is an important open problem in verification, automata, and complexity theory. In this paper, we develop an abstract setting for studying and solving such games, based on function optimization over certain discrete structures. We introduce new classes of recursively local-global (RLG) and partial recursively local-global (PRLG) functions, and show that strategy evaluation functions for simple
more » ... ic, mean payoff, and parity games belong to these classes. In this setting, we suggest randomized subexponential algorithms appropriate for RLG-and PRLG-function optimization. We show that the subexponential algorithms for combinatorial linear programming, due to Kalai and Matoušek, Sharir, Welzl, can be adapted for optimizing the RLG-and PRLG-functions.
doi:10.1016/j.tcs.2005.07.041 fatcat:u3gsujjxkjflzfu5ndcr6cgqru