On the Topological Complexity of Weakly Recognizable Tree Languages
نویسندگان
چکیده
We show that the family of tree languages recognized by weak alternating automata is closed by three set theoretic operations that correspond to sum, multiplication by ordinals < ω, and pseudoexponentiation with the base ω1 of the Wadge degrees. In consequence, the Wadge hierarchy of weakly recognizable tree languages has the height of at least ε0, that is the least fixed point of the exponentiation with the base ω.
منابع مشابه
On the topological complexity of tree languages
The article surveys recent results in the study of topological complexity of recognizable tree languages. Emphasis is put on the relation between topological hierarchies, like the Borel hierarchy or the Wadge hierarchy, and the hierarchies resulting from the structure of automata, as the Rabin-Mostowski index hierarchy. The topological complexity of recognizable tree languages is seen as an evi...
متن کاملOn Recognizable Tree Languages Beyond the Borel Hierarchy
We investigate the topological complexity of non Borel recognizable tree languages with regard to the difference hierarchy of analytic sets. We show that, for each integer n ≥ 1, there is a Dωn(Σ 1 1)-complete tree language Ln accepted by a (non deterministic) Muller tree automaton. On the other hand, we prove that a tree language accepted by an unambiguous Büchi tree automaton must be Borel. T...
متن کاملTREE AUTOMATA BASED ON COMPLETE RESIDUATED LATTICE-VALUED LOGIC: REDUCTION ALGORITHM AND DECISION PROBLEMS
In this paper, at first we define the concepts of response function and accessible states of a complete residuated lattice-valued (for simplicity we write $mathcal{L}$-valued) tree automaton with a threshold $c.$ Then, related to these concepts, we prove some lemmas and theorems that are applied in considering some decision problems such as finiteness-value and emptiness-value of recognizable t...
متن کاملOn the Complexity of the Syntax of Tree Languages
The syntactic complexity of a tree language is defined according to the number of the distinct syntactic classes of all trees with a fixed yield length. This leads to a syntactic classification of tree languages and it turns out that the class of recognizable tree languages is properly contained in that of languages with bounded complexity. A refined syntactic complexity notion is also presente...
متن کاملAn upper bound on the complexity of recognizable tree languages
The third author noticed in his 1992 PhD Thesis [Sim92] that every regular tree language of infinite trees is in a class a(Dn(Σ2)) for some natural number n ≥ 1, where a is the game quantifier. We first give a detailed exposition of this result. Next, using an embedding of the Wadge hierarchy of non self-dual Borel subsets of the Cantor space 2 into the class ∆2, and the notions of Wadge degree...
متن کامل