Alternating Tree Automata, Parity Games, and Modal -Calculus
نویسنده
چکیده
2 From Modal -Calculus to Alternating Tree Automata 4 2.1 Modal -Calculus . . . . . . . . . . . . . . . . . . . . . . . . . . 5 2.1.1 Kripke Structures . . . . . . . . . . . . . . . . . . . . . . 5 2.1.2 Syntax . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 2.1.3 Substitution . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.1.4 Semantics . . . . . . . . . . . . . . . . . . . . . . . . . . 7 2.1.5 Query-Based Semantics . . . . . . . . . . . . . . . . . . 8 2.1.6 Fixed Point Alternation . . . . . . . . . . . . . . . . . . . 10 2.2 Alternating Tree Automata . . . . . . . . . . . . . . . . . . . . . 11 2.2.1 Informal Description . . . . . . . . . . . . . . . . . . . . 11 2.2.2 Formal Definition . . . . . . . . . . . . . . . . . . . . . . 12 2.2.3 Runs . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12 2.2.4 Acceptance . . . . . . . . . . . . . . . . . . . . . . . . . 13 2.2.5 Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 2.3 From -Calculus to Alternating Tree Automata . . . . . . . . . . 14 2.3.1 The Conversion . . . . . . . . . . . . . . . . . . . . . . . 14 2.3.2 Proof of Correctness . . . . . . . . . . . . . . . . . . . . 15 This paper resulted from an invited talk given at the Journées Montoises, Marne-la-Vallée, March 2000.
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تاریخ انتشار 2000