Decidability and Closure Properties of Equational Tree Languages
نویسندگان
چکیده
Equational tree automata provide a powerful tree language framework that facilitates to recognize congruence closures of tree languages. In the paper we show the emptiness problem for AC-tree automata and the intersection-emptiness problem for regular AC-tree automata, each of which was open in our previous work [20], are decidable, by a straightforward reduction to the reachability problem for ground AC-term rewriting. The newly obtained results generalize decidability of so-called reachable property problem of Mayr and Rusinowitch [17]. We then discuss complexity issue of AC-tree automata. Moreover, in order to solve some other questions about regular Aand AC-tree automata, we recall the basic connection between word languages and tree languages.
منابع مشابه
Languages Modulo Normalization
We propose a new class of tree automata, called tree automata with normalization (TAN). This framework extends equational tree automata, and improved the results of them: recognized tree languages modulo the idempotency f(x, x) = x are closed under complement, besides we do not lose an important decidability result. In the paper, first we investigate the closure properties of this class for Boo...
متن کاملEquational Formulae with Membership Constraints
We propose a set of transformation rules for rst order formulae whose atoms are either equations between terms or \membership constraints" t 2. can be interpreted as a regular tree language (is called a sort in the algebraic speciication community) or as a tree language in any class of languages which satisses some adequate closure and decidability properties. This set of rules is proved to be ...
متن کاملMultidimensional fuzzy finite tree automata
This paper introduces the notion of multidimensional fuzzy finite tree automata (MFFTA) and investigates its closure properties from the area of automata and language theory. MFFTA are a superclass of fuzzy tree automata whose behavior is generalized to adapt to multidimensional fuzzy sets. An MFFTA recognizes a multidimensional fuzzy tree language which is a regular tree language so that for e...
متن کاملCombining Equational Tree Automata over AC and ACI Theories
In this paper, we study combining equational tree automata in two different senses: (1) whether decidability results about equational tree automata over disjoint theories E1 and E2 imply similar decidability results in the combined theory E1 ∪ E2; (2) checking emptiness of a language obtained from the Boolean combination of regular equational tree languages. We present a negative result for the...
متن کاملBeyond Regularity: Equational Tree Automata for Associative and Commutative Theories
A new tree automata framework, called equational tree automata, is presented. In the newly introduced setting, congruence closures of recognizable tree languages are recognizable. Furthermore, we prove that in certain useful cases, recognizable tree languages are closed under union and intersection. To compare with early related work, e.g. [7], we discuss the relationship between linear bounded...
متن کامل