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A note on the avoidability of binary patterns with variables and reversals

2015/08/19 by Robert Mercaş, Mercaş, Robert
Biochemistry, Genetics and Molecular Biology · Computer Science · #Advanced Algebra and Logic #DNA and Biological Computing #FOS: Computer and information sciences #Formal Languages and Automata Theory (cs.FL) #Logic, programming, and type systems #cs.FL #semigroups and automata theory

paper · pdf · doi:10.48550/arxiv.1508.04571

This work is mostly obsolete as a week ago Currie and Lafrance fully characterised the patterns with reversals in [http://arxiv.org/abs/1508.02101]. The only novelty of this work is given by the aperiodicity restriction of the infinite words avoiding such patterns

arxiv created 2015/08/19 · openalex publication_date 2015/08/19 · arxiv updated 2015/08/20 · openalex created_date 2022/10/01 · openalex updated_date 2026/07/28

Abstract

In this note we present a characterisation of all unary and binary patterns that do not only contain variables, but also reversals of their instances. These types of variables were studied recently in either more general or particular cases. We show that the results are not surprising at all in the general case, and extend the avoidability of these patterns to enforce aperiodic words.

Citations

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