6 research outputs found
Templates for the k-binomial complexity of the Tribonacci word
Consider k-binomial equivalence: two finite words are equivalent if they share the same subwords of length at most k with the same multiplicities. With this relation, the k-binomial complexity of an infinite word x maps the integer n to the number of pairwise non-equivalent factors of length n occurring in x. In this paper based on the notion of template introduced by Currie et al., we show that, for all k≥2, the k-binomial complexity of the Tribonacci word coincides with its usual factor complexity p(n)=2n+1. A similar result was already known for Sturmian words, but the proof relies on completely different techniques that seemingly could not be applied for Tribonacci. © 2019 Elsevier Inc
Computing the k-binomial complexity of the Tribonacci word
Oral presentation of the associated paper that was published in the conference proceeding
Some Tribonacci Conjectures
In a recent talk of Robbert Fokkink, some conjectures related to the infinite
Tribonacci word were stated by the speaker and the audience. In this note we
show how to prove (or disprove) the claims easily in a "purely mechanical"
fashion, using the Walnut theorem-prover
Binomial Complexities and Parikh-Collinear Morphisms
peer reviewedTwo words are k-binomially equivalent, if each word of length at most k occurs as a subword, or scattered factor, the same number of times in both words. The k-binomial complexity of an infinite word maps the natural n to the number of k-binomial equivalence classes represented by its factors of length n. Inspired by questions raised by Lejeune, we study the relationships between the k and (k+1)-binomial complexities; as well as the link with the usual factor complexity. We show that pure morphic words obtained by iterating a Parikh-collinear morphism, i.e. a morphism mapping all words to words with bounded abelian complexity, have bounded k-binomial complexity. In particular, we study the properties of the image of a Sturmian word by an iterate of the Thue-Morse morphism
Computer Aided Verification
This open access two-volume set LNCS 13371 and 13372 constitutes the refereed proceedings of the 34rd International Conference on Computer Aided Verification, CAV 2022, which was held in Haifa, Israel, in August 2022. The 40 full papers presented together with 9 tool papers and 2 case studies were carefully reviewed and selected from 209 submissions. The papers were organized in the following topical sections: Part I: Invited papers; formal methods for probabilistic programs; formal methods for neural networks; software Verification and model checking; hyperproperties and security; formal methods for hardware, cyber-physical, and hybrid systems. Part II: Probabilistic techniques; automata and logic; deductive verification and decision procedures; machine learning; synthesis and concurrency. This is an open access book
Templates for the k-binomial complexity of the Tribonacci word
Consider the k-binomial equivalence: two finite words are equivalent if they share the same subwords of length at most k with the same multiplicities. With this relation, the k-binomial complexity of an infinite word x maps the integer n to the number of pairwise non-equivalent factors of length n occurring in x. In this paper based on the notion of template introduced by Currie et al., we show that, for all k > 1, the k-binomial complexity of the Tribonacci word coincides with its usual factor complexity p(n)=2n+1. A similar result was already known for Sturmian words but the proof relies on completely different techniques that seemingly could not be applied for Tribonacci