On the Morse-Hedlund complexity gap

2009/03/09 by Cassaigne, Julien, Nicolas, Francois
#Discrete Mathematics (cs.DM) #FOS: Computer and information sciences #Formal Languages and Automata Theory (cs.FL)

paper · doi:10.48550/arxiv.0903.1627

Abstract

In 1938, Morse and Hedlund proved that the subword complexity function of an infinite word is either bounded or at least linearly growing. In 1982, Ehrenfeucht and Rozenberg proved that this gap property holds for the subword complexity function of any language. The aim of the present paper is to present a self-contained, compact proof of Ehrenfeucht and Rozenberg's result.

Related

• Subword complexity and decomposition of the set of factors
• Frequencies of subwords in words of linear subword complexity
• On the complexity of subshifts and infinite words
• The subword complexity of a class of infinite binary words
• On the shape of subword complexity sequences of finite words