Related papers: An Upper Bound on the Complexity of Recognizable T…
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 $n \geq 1$, there is a $D_{\omega^n}({\bf \Sigma}^1_1)$-complete…
In this article we provide effective characterisations of regular languages of infinite trees that belong to the low levels of the Wadge hierarchy. More precisely we prove decidability for each of the finite levels of the hierarchy; for the…
We show that it is decidable whether a given a regular tree language belongs to the class ${\bf \Delta^0_2}$ of the Borel hierarchy, or equivalently whether the Wadge degree of a regular tree language is countable.
The game tree languages can be viewed as an automata-theoretic counterpart of parity games on graphs. They witness the strictness of the index hierarchy of alternating tree automata, as well as the fixed-point hierarchy over binary trees.…
This work is a study of the expressive power of unambiguity in the case of automata over infinite trees. An automaton is called unambiguous if it has at most one accepting run on every input, the language of such an automaton is called an…
We provide a complete description of the Wadge hierarchy for deterministically recognisable sets of infinite trees. In particular we give an elementary procedure to decide if one deterministic tree language is continuously reducible to…
We study tree languages that can be defined in \Delta_2 . These are tree languages definable by a first-order formula whose quantifier prefix is forall exists, and simultaneously by a first-order formula whose quantifier prefix is . For the…
For a given regular language of infinite trees, one can ask about the minimal number of priorities needed to recognize this language with a non-deterministic, alternating, or weak alternating parity automaton. These questions are known as,…
An automaton is unambiguous if for every input it has at most one accepting computation. An automaton is k-ambiguous (for k > 0) if for every input it has at most k accepting computations. An automaton is boundedly ambiguous if it is…
We show that it is decidable whether two regular languages of infinite trees are separable by a deterministic language, resp., a game language. We consider two variants of separability, depending on whether the set of priorities of the…
We consider the problem of computing the probability of regular languages of infinite trees with respect to the natural coin-flipping measure. We propose an algorithm which computes the probability of languages recognizable by \emph{game…
The class of Boolean combinations of tree languages recognized by deterministic top-down tree automata (also known as deterministic root-to-frontier automata) is studied. The problem of determining for a given regular tree language whether…
We propose a new algebraic framework to discuss and classify recognizable tree languages, and to characterize interesting classes of such languages. Our algebraic tool, called preclones, encompasses the classical notion of syntactic…
We explore from an algebraic viewpoint the properties of the tree languages definable with a first-order formula involving the ancestor predicate, using the description of these languages as those recognized by iterated block products of…
$\omega$-clones are multi-sorted structures that naturally emerge as algebras for infinite trees, just as $\omega$-semigroups are convenient algebras for infinite words. In the algebraic theory of languages, one hopes that a language is…
We consider finite trees with edges labeled by letters on a finite alphabet $\varSigma$. Each pair of nodes defines a unique labeled path whose trace is a word of the free monoid $\varSigma^*$. The set of all such words defines the language…
The parity index problem of tree automata asks, given a regular tree language $L$ and a set of priorities $J$, is $L$ $J$-feasible, that is, recognised by a nondeterministic parity automaton with priorities $J$? This is a long-standing open…
Due to the works of S. Bozapalidis and A. Alexandrakis, there is a well-known characterization of recognizable weighted tree languages over fields in terms of finite-dimensionality of syntactic vector spaces. Here we prove a…
We study the notion of sparseness for regular languages over finite trees and infinite words. A language of trees is called sparse if the relative number of $n$-node trees in the language tends to zero, and a language of infinite words is…
We study the matching problem of regular tree languages, that is, "$\exists \sigma:\sigma(L)\subseteq R$?" where $L,R$ are regular tree languages over the union of finite ranked alphabets $\Sigma$ and $\mathcal{X}$ where $\mathcal{X}$ is an…