DLT 2016: Developments in Language Theory pp 344-354

Avoidability of Formulas with Two Variables

• Pascal Ochem
• Matthieu Rosenfeld
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9840)

Abstract

In combinatorics on words, a word w over an alphabet $$\varSigma$$ is said to avoid a pattern p over an alphabet $$\varDelta$$ of variables if there is no factor f of w such that $$f=h(p)$$ where $$h\,{:}\,\varDelta ^*\rightarrow \varSigma ^*$$ is a non-erasing morphism. A pattern p is said to be k-avoidable if there exists an infinite word over a k-letter alphabet that avoids p. We consider the patterns such that at most two variables appear at least twice, or equivalently, the formulas with at most two variables. For each such formula, we determine whether it is 2-avoidable.

Keywords

Word Pattern avoidance

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