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  • セイヤク ツキ キオートマトン ト ソノ ヘイホウセイ
  • Tree Automata with Constraints and their Closure-Properties

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木オートマトンは項を入力としたオートマトンであり,和集合・補集合・積集合演算に閉じていることや空判定問題が決定可能であることから,項書換え系の性質を調べることに有効である.また,近年,制約付き項書換え系に関する研究が行われており,特に定理自動証明の研究が注目されている.本稿では,等号不等号制約付き木オートマトンの制約を任意の制約系を指定できるように一般化した制約付き木オートマトンを提案し,任意の制約付き木オートマトンに対して決定性と完全性を持ち受理集合が等価である制約付き木オートマトンが存在することを示す.さらに,制約付き木オートマトンのクラスが和・積・補集合演算に閉じていることを示す. Tree automata are useful in analyzing properties of term rewriting systems since the class of recognizable tree languages is closed under union, intersection and complement and since the emptiness problem is decidable. Recently, constrained term rewriting systems are investigated and theorem proving methods of contrained systems attract attention. In this paper, by generalizing tree automata with equality and disequality constraints, we propose tree automata with constraints, for which one can specify structures that give an interpretation of predicate symbols and some function symbols. We also show that for every tree automaton with constraints there exists a deterministic and complete tree automaton with constraints, which recognizes the tree language recognized by the former one. In addition, we show that the class of recognized tree languages for tree automata with constraints is closed under union, intersection and complement.




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