Related papers: On primary and secondary repetitions in words
We give a first-order definition of key polynomials, we show the links with previous definitions, that it is relevant to study key degrees, and to use a kind of valuations that we call partially multiplicative. We also prove or reprove…
If an infinite non-periodic word is uniformly recurrent or is of bounded repetition, then the limit of its periodicity complexity is infinity. Moreover, there are uniformly recurrent words with the periodicity complexity arbitrarily high at…
This paper examines the characterization and learning of grammars defined with enriched representational models. Model-theoretic approaches to formal language theory traditionally assume that each position in a string belongs to exactly one…
We study the second law in the context of combinatorial processes, focusing on the mechanisms that give rise to irreversible behavior from an underlying deterministic, invertible, and reversible dynamics.
Given a countable set X (usually taken to be N or Z), an infinite permutation $\pi$ of X is a linear ordering $<_\pi$ of X. This paper investigates the combinatorial complexity of infinite permutations on N associated with the image of…
The physics of randomness and regularities for languages (mother tongues) and their lifetimes and family trees and for the second languages are studied in terms of two opposite processes; random multiplicative noise [1], and fragmentation…
We consider the termination/non-termination property of a class of loops. Such loops are commonly used abstractions of real program pieces. Second-order logic is a convenient language to express non-termination. Of course, such property is…
In this paper we provide an overview of a series of recent results regarding algorithms for searching for subsequences in words or for the analysis of the sets of subsequences occurring in a word.
The fundamental properties of biquaternions (complexified quaternions) are presented including several different representations, some of them new, and definitions of fundamental operations such as the scalar and vector parts, conjugates,…
A run in a word is a periodic factor whose length is at least twice its period and which cannot be extended to the left or right (by a letter) to a factor with greater period. In recent years a great deal of work has been done on estimating…
A repetition is a response that repeats words in the previous speaker's utterance in a dialogue. Repetitions are essential in communication to build trust with others, as investigated in linguistic studies. In this work, we focus on…
We extend classical theorems of Renyi by finding the distributions of the numbers of both weak and strong left-to-right maxima (a.k.a. outstanding elements) in words over a given alphabet and in permutations of a given multiset.
In combinatorial optimization, partial variable assignments are called persistent if they agree with some optimal solution. We propose persistency criteria for the multicut and max-cut problem as well as fast combinatorial routines to…
Primitive recursion, mu-recursion, universal object and universe theories, complexity controlled iteration, code evaluation, soundness, decidability, G\"odel incompleteness theorems, inconsistency provability for set theory, constructive…
The set of prime numbers has been analyzed, based on their algebraic and arithmetical structure. Here by obtaining a sort of linear formula for the set of prime numbers, they are redefined and identified; under a systematic procedure it has…
By an analogy to the duality between the recurrence time and the longest match length, we introduce a quantity dual to the maximal repetition length, which we call the repetition time. Extending prior results, we sandwich the repetition…
In this paper we study prime, maximal and two--class congruences from the point of view of the relationships between them in various kinds of universal algebras, as well as their direct and inverse images through morphisms. This research…
We define the notion of circular words, then consider on such words a constraint derived from the Fibonacci condition. We give several results on the structure of these circular words, then mention possible applications to various…
The sequential structure of language, and the order of words in a sentence specifically, plays a central role in human language processing. Consequently, in designing computational models of language, the de facto approach is to present…
Generalizations of linear numeration systems in which the set of natural numbers is recognizable by finite automata are obtained by describing an arbitrary infinite regular language following the lexicographic ordering. For these systems of…