Related papers: Closures in Formal Languages: Concatenation, Separ…
A wide range of constraints can be compactly specified using automata or formal languages. In a sequence of recent papers, we have shown that an effective means to reason with such specifications is to decompose them into primitive…
Over finite words, languages of dot-depth one are expressively complete for alternation-free first-order logic. This fragment is also known as the Boolean closure of existential first-order logic. Here, the atomic formulas comprise order,…
We introduce a meta-model based on formal languages, dubbed formal choreographic languages, to study message-passing systems. Our framework allows us to generalise standard constructions from the literature and to compare them. In…
We investigate the star-free closure, which associates to a class of languages its closure under Boolean operations and marked concatenation. We prove that the star-free closure of any finite class and of any class of groups languages with…
For fragments L of first-order logic (FO) with counting quantifiers, we consider the definability problem, which asks whether a given L-formula can be equivalently expressed by a formula in some fragment of L without counting, and the more…
The separating words problem asks for the size of the smallest DFA needed to distinguish between two words of length <= n (by accepting one and rejecting the other). In this paper we survey what is known and unknown about the problem,…
The requirement of a language to be conditionally decomposable is imposed on a specification language in the coordination supervisory control framework of discrete-event systems. In this paper, we present a polynomial-time algorithm for the…
We introduce the notion of topological entropy of a formal languages as the topological entropy of the minimal topological automaton accepting it. Using a characterization of this notion in terms of approximations of the Myhill-Nerode…
We consider some questions about formal languages that arise when inverses of letters, words and languages are defined. The reduced representation of a language over the free monoid is its unique equivalent representation in the free group.…
Trapezoidal words are finite words having at most n+1 distinct factors of length n, for every n>=0. They encompass finite Sturmian words. We distinguish trapezoidal words into two disjoint subsets: open and closed trapezoidal words. A…
Contemporary deep learning models effectively handle languages with diverse morphology despite not being directly integrated into them. Morphology and word order are closely linked, with the latter incorporated into transformer-based models…
The computational complexity of the isomorphism problem for regular trees, regular linear orders, and regular words is analyzed. A tree is regular if it is isomorphic to the prefix order on a regular language. In case regular languages are…
We study the sweep complexity of DFA in one-way jumping mode answering several questions posed earlier. This measure is the number of times in the worst case that such machines have to return to the beginning of their input after having…
For every class $\mathscr{C}$ of word languages, one may associate a decision problem called $\mathscr{C}$-separation. Given two regular languages, it asks whether there exists a third language in $\mathscr{C}$ containing the first…
A deterministic finite automaton (DFA) is composite if its language can be decomposed into an intersection of languages of smaller DFAs. Otherwise, A is prime. This notion of primality was introduced by Kupferman and Mosheiff in 2013, and…
We study modal separability for fixpoint formulae: given two mutually exclusive fixpoint formulae $\varphi,\varphi'$, decide whether there is a modal formula $\psi$ that separates them, that is, that satisfies…
We identify a subclass of the regular commutative languages that is closed under the iterated shuffle, or shuffle closure. In particular, it is regularity-preserving on this subclass. This subclass contains the commutative group languages…
The separability problem for word languages of a class $\mathcal{C}$ by languages of a class $\mathcal{S}$ asks, for two given languages $I$ and $E$ from $\mathcal{C}$, whether there exists a language $S$ from $\mathcal{S}$ that includes…
In earlier work a description of a physical entity is given by means of a state property system and it is proven that any state property system is equivalent to a closure space. In the present paper we investigate the relations between…
Context-free language theory is a well-established area of mathematics, relevant to computer science foundations and technology. This paper presents the preliminary results of an ongoing formalization project using context-free grammars and…