Combinatorial structure and randomized subexponential algorithms for infinite games

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 certai...

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Published in:Theoretical computer science Vol. 349; no. 3; pp. 347 - 360
Main Authors: Björklund, Henrik, Vorobyov, Sergei
Format: Journal Article
Language:English
Published: Amsterdam Elsevier B.V 16.12.2005
Elsevier
Subjects:
Algorithmics. Computability. Computer arithmetics
Applied sciences
Calculus of variations and optimal control
Combinatorial linear programming
Completely unimodal functions
Computer science; control theory; systems
Exact sciences and technology
Game theory
Mathematical analysis
Mathematical programming
Mathematics
Mean payoff games
Operational research and scientific management
Operational research. Management science
Parity games
Pseudo-Boolean optimization
Randomized algorithms
Sciences and techniques of general use
Simple stochastic games
Theoretical computing
Parity games
Simple stochastic games
Pseudo-Boolean optimization
Completely unimodal functions
Combinatorial linear programming
Randomized algorithms
Mean payoff games
Computer theory
Parity game
Mean playoff game
Optimization method
Combinatorial algorithm
Linear programming
Verification
Pseudo boolean optimization
Function evaluation
Stochastic game
Automata theory
Strategy
Mean payoff games: Simple stochastic games
ISSN:0304-3975, 1879-2294
Online Access:Get full text
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Summary: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 stochastic, 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.
Bibliography:ObjectType-Article-2
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ISSN:0304-3975
1879-2294
DOI:10.1016/j.tcs.2005.07.041