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Randomized Subexponential Algorithms for Infinite Games (2004)
| Citations: | 6 - 0 self |
BibTeX
@MISC{Björklund04randomizedsubexponential,
author = {Henrik Björklund and Sven Sandberg and Sergei Vorobyov},
title = { Randomized Subexponential Algorithms for Infinite Games},
year = {2004}
}
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Abstract
The complexity of solving infinite games, including parity, mean payoff, and simple stochastic games, is an important open problem in verification, automata theory, and complexity theory. In this paper we develop an abstract setting for studying and solving such games, as well as related problems, based on function optimization over certain discrete structures. We introduce new classes of completely local-global (CLG) and recursively local-global (RLG) functions, and show that strategy evaluation functions for parity and simple stochastic games belong to these classes. We also establish a relation to the previously well-studied completely unimodal (CU) and local-global functions. A number of nice properties of CLG-functions are proved. In this setting, we survey several randomized optimization algorithms appropriate for CU-, CLG-, and RLG-functions. We show that the subexponential algorithms for linear programming by Kalai and Matouˇsek, Sharir, and Welzl, can be adapted to optimizing the functions we study, with preserved subexponential expected running time. We examine the relations to two other abstract frameworks for subexponential
Keyphrases
infinite game subexponential algorithm simple stochastic game matou sek function optimization nice property certain discrete structure new class local-global function important open problem abstract setting automaton theory related problem strategy evaluation function running time abstract framework linear programming complexity theory
