Related papers: Cross-bifix-free sets via Motzkin paths generation
Canonical inference rules and canonical systems are defined in the framework of non-strict single-conclusion sequent systems, in which the succeedents of sequents can be empty. Important properties of this framework are investigated, and a…
In this paper we show that there exists an uncountable family of finitely generated simple groups with the same positive theory as any non-abelian free group. In particular, these simple groups have infinite $w$-verbal width for all…
In this paper, we construct a uniformely recurrent infinite word of low complexity without uniform frequencies of letters. This shows the optimality of a bound of Boshernitzan, which gives a sufficient condition for a uniformly recurrent…
Morpho-syntactic lexicons provide information about the morphological and syntactic roles of words in a language. Such lexicons are not available for all languages and even when available, their coverage can be limited. We present a…
For the first time we construct an infinite family of Kochen-Specker sets in a space of fixed dimension, namely in R^4. While most of the previous constructions of Kochen-Specker sets have been based on computer search, our construction is…
A prefix normal word is a binary word with the property that no substring has more $1$s than the prefix of the same length. By proving that the set of prefix normal words is a bubble language, we can exhaustively list all prefix normal…
We entirely classify definable sets up to definable bijections in $\mathbb{Z}$-groups, where the language is the one of ordered abelian groups. From this, we deduce, among others, a classification of definable families of bounded definable…
We introduce a flexible class of well-quasi-orderings (WQOs) on words that generalizes the ordering of (not necessarily contiguous) subwords. Each such WQO induces a class of piecewise testable languages (PTLs) as Boolean combinations of…
We introduce and study the model of simply generated non-crossing partitions, which are, roughly speaking, chosen at random according to a sequence of weights. This framework encompasses the particular case of uniform non-crossing…
This letter presents a direct construction of cross Z-complementary sequence sets (CZCSSs), whose aperiodic correlation sums exhibit zero correlation zones at both the front-end and tail-end shifts. CZCSS can be regarded as an extension of…
We consider words over a binary alphabet. A word $w$ is overlap-free if it does not have factors (blocks of consecutive letters) of the form $uvuvu$ for nonempty $u$. Let $M(w)$ denote the number of positions that are middle positions of…
Iterated hairpin completion is an operation on formal languages that is inspired by the hairpin formation in DNA biochemistry. Iterated hairpin completion of a word (or more precisely a singleton language) is always a context-sensitive…
An aggregative composition is a binary operation obeying the principle that the whole is determined by the sum of its parts. The development of graph algebras, on which the theory of formal graph languages is built, relies on aggregative…
Symmetric fix-free codes are prefix condition codes in which each codeword is required to be a palindrome. Their study is motivated by the topic of joint source-channel coding. Although they have been considered by a few communities they…
In this paper, we will explicitly construct cofree coalgebras, by first constructing cofree precoalgebras (namely those not necessarily coassociative or counital). Our approach does not impose any condition to the coefficient ring, which…
We introduce a class of fixed points of primitive morphisms among aperiodic binary generalized pseudostandard words. We conjecture that this class contains all fixed points of primitive morphisms among aperiodic binary generalized…
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…
In this paper we address the decision problem for a fragment of set theory with restricted quantification which extends the language studied in [4] with pair related quantifiers and constructs, in view of possible applications in the field…
For any context-free grammar, we build a transition diagram, that is, a finite directed graph with labeled arcs, which describes the work of the grammar. This approach is new, and it is different from previously known graph models. We…
Context-free grammar simplification is a subject of high importance in computer language processing technology as well as in formal language theory. This paper presents a formalization, using the Coq proof assistant, of the fact that…