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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Veröffentlicht in:	Theoretical computer science Jg. 349; H. 3; S. 347 - 360
Hauptverfasser:	Björklund, Henrik, Vorobyov, Sergei
Format:	Journal Article
Sprache:	Englisch
Veröffentlicht:	Amsterdam Elsevier B.V 16.12.2005 Elsevier
Schlagworte:	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
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Abstract	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.
AbstractList	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. 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 Matousek, Sharir, Welzl, can be adapted for optimizing the RLG- and PRLG- functions.
Author	Björklund, Henrik Vorobyov, Sergei
Author_xml	– sequence: 1 givenname: Henrik surname: Björklund fullname: Björklund, Henrik – sequence: 2 givenname: Sergei surname: Vorobyov fullname: Vorobyov, Sergei email: Sergei.Vorobyov@it.uu.se
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Keywords	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
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Snippet	The complexity of solving infinite games, including parity, mean payoff, and simple stochastic, is an important open problem in verification, automata, and...
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SubjectTerms	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
Title	Combinatorial structure and randomized subexponential algorithms for infinite games
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