Related papers: The Boolean Hierarchy over Level 1/2 of the Straub…

The purpose of this paper is to provide efficient algorithms that decide membership for classes of several Boolean hierarchies for which efficiency (or even decidability) were previously not known. We develop new forbidden-chain…

We consider the class of languages defined in the 2-variable fragment of the first-order logic of the linear order. Many interesting characterizations of this class are known, as well as the fact that restricting the number of quantifier…

We show that for any $i > 0$, it is decidable, given a regular language, whether it is expressible in the $\Sigma_i[<]$ fragment of first-order logic FO[<]. This settles a question open since 1971. Our main technical result relies on the…

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…

Let A be a finite alphabet and let L contained in (A*)^n be an n-variable language over A. We say that L is regular if it is the language accepted by a synchronous n-tape finite state automaton, it is quasi-regular if it is accepted by an…

The study of various decision problems for logic fragments has a long history in computer science. This paper is on the membership problem for a fragment of first-order logic over infinite words; the membership problem asks for a given…

In the paper hereditary classes of ${\rm L}$-structures are studied with language of the form ${{\rm L} = {\rm L_{fin}} \cup {\rm L_\infty}}$, where ${{\rm L_{fin}} = \langle R_1,R_2,\ldots, R_m, = \rangle}$ and ${{\rm L_\infty} = \langle…

We consider the two-variable fragment FO^2[<] of first-order logic over finite words. Numerous characterizations of this class are known. Th\'erien and Wilke have shown that it is decidable whether a given regular language is definable in…

We show that the decidability of the first-order theory of the language that combines Boolean algebras of sets of uninterpreted elements with Presburger arithmetic operations. We thereby disprove a recent conjecture that this theory is…

A class of languages C is perfect if it is closed under Boolean operations and the emptiness problem is decidable. Perfect language classes are the basis for the automata-theoretic approach to model checking: a system is correct if the…

This work is concerned with regular languages defined over large alphabets, either infinite or just too large to be expressed enumeratively. We define a generic model where transitions are labeled by elements of a finite partition of the…

A regular language L is said to be cellular if there exists a 1-dimensional cellular automaton CA such that L is the language consisting of the finite blocks associated with CA. It is shown that cellularity of a regular language is…

We define a new class of languages of $\omega$-words, strictly extending $\omega$-regular languages. One way to present this new class is by a type of regular expressions. The new expressions are an extension of $\omega$-regular expressions…

For any first order theory T we construct a Boolean valued model M, in which precisely the T--provable formulas hold, and in which every (Boolean valued) subset which is invariant under all automorphisms of M is definable by a first order…

We consider first-order logic over the subword ordering on finite words, where each word is available as a constant. Our first result is that the $\Sigma_1$ theory is undecidable (already over two letters). We investigate the decidability…

We investigate the complexity of the separation problem associated to classes of regular languages. For a class C, C-separation takes two regular languages as input and asks whether there exists a third language in C which includes the…

We define a class of languages of infinite words over infinite alphabets, and the corresponding automata. The automata used for recognition are a generalisation of deterministic Muller automata to the setting of nominal sets. Remarkably,…

This paper studies the complexity of operations on finite automata and the complexity of their decision problems when the alphabet is unary. Let $n$ denote the maximum of the number of states of the input finite automata considered in the…

Concatenation hierarchies are classifications of regular languages. All such hierarchies are built through the same construction process: start from an initial class of languages and build new levels using two generic operations.…

We show that the first-order logical theory of the binary overlap-free words (and, more generally, the ${\alpha}$-free words for rational ${\alpha}$, $2 < {\alpha} \leq 7/3$), is decidable. As a consequence, many results previously obtained…