Related papers: Star-free languages and local divisors
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…
We introduce an operator on classes of regular languages, the star-free closure. Our motivation is to generalize standard results of automata theory within a unified framework. Given an arbitrary input class $C$, the star-free closure…
In this article we show that every group with a finite presentation satisfying one or both of the small cancellation conditions $C'(1/6)$ and $C'(1/4)-T(4)$ has the property that the set of all geodesics (over the same generating set) is a…
The famous theorem by Chomsky and Sch\"utzenberger (CST) says that every context-free language $L$ over an alphabet $\Sigma$ is representable as $h(D \cap R)$, where $D$ is a Dyck language over a set $\Omega$ of brackets, $R$ is a local…
Let U be a numeration system, a set X of integers is U-star-free if the set made up of the U-representations of the elements in X is a star-free regular language. Answering a question of A. de Luca and A. Restivo, we obtain a complete…
A language $L$ is said to be ${\cal C}$-measurable, where ${\cal C}$ is a class of languages, if there is an infinite sequence of languages in ${\cal C}$ that ``converges'' to $L$. We investigate the properties of ${\cal C}$-measurability…
We describe two formalisms for defining graph languages, and prove that they are equivalent: 1. Separator logic. This is first-order logic on graphs which is allowed to use the edge relation, and for every $n \in \{0,1,\ldots \}$ a relation…
The class of Church-Rosser congruential languages has been introduced by McNaughton, Narendran, and Otto in 1988. A language L is Church-Rosser congruential (belongs to CRCL), if there is a finite, confluent, and length-reducing semi-Thue…
The Sch\"utzenberger product of monoids is a key tool for the algebraic treatment of language concatenation. In this paper we generalize the Sch\"utzenberger product to the level of monoids in an algebraic category $\mathscr{D}$, leading to…
Separation is a classical problem asking whether, given two sets belonging to some class, it is possible to separate them by a set from a smaller class. We discuss the separation problem for regular languages. We give a Ptime algorithm to…
A monoid is called special if it admits a presentation in which all defining relations are of the form $w = 1$. Every group is special, but not every monoid is special. In this article, we describe the language-theoretic properties of the…
We consider first-order logic with monoidal quantifiers over words. We show that all languages with a neutral letter, definable using the addition numerical predicate are also definable with the order predicate as the only numerical…
A classic result in formal language theory is the equivalence among non-counting, or aperiodic, regular languages, and languages defined through star-free regular expressions, or first-order logic. Past attempts to extend this result beyond…
The problem considered in this paper is whether an inequality of omega-terms is valid in a given level of a concatenation hierarchy of star-free languages. The main result shows that this problem is decidable for all (integer and half)…
A zero-one language L is a regular language whose asymptotic probability converges to either zero or one. In this case, we say that L obeys the zero-one law. We prove that a regular language obeys the zero-one law if and only if its…
Group languages are regular languages recognized by finite groups, or equivalently by finite automata in which each letter induces a permutation on the set of states. We investigate the separation problem for this class of languages: given…
The dot-depth hierarchy is a classification of star-free languages. It is related to the quantifier alternation hierarchy of first-order logic over finite words. We consider fragments of languages with dot-depth 1/2 and dot-depth 1 obtained…
A star anagram is a rearrangement of the letters of one word to produce another word where no letter retains its original neighbors. These maximally shuffled anagrams are rare, comprising only about 5.7% of anagrams in English. They can…
We prove that for any sequence of binary alphabets $\mathcal{A}_1,\mathcal{A}_2,\dots$, there exists a cube-free word $c_1c_2\dots$ so that $c_1\in\mathcal{A}_1,c_2\in\mathcal{A}_2,\dots$. In particular, for every $n$, there are at least…
We prove a Chomsky-Sch\"utzenberger representation theorem for multiple context-free languages weighted over complete commutative strong bimonoids.