Comparing Complexity Functions of a Language and Its Extendable Part

Issue		RAIRO-Theor. Inf. Appl. Volume 42, Number 3, July-September 2008 JM'06


Page(s)		647 - 655
DOI		10.1051/ita:2008021
Published online		03 June 2008

RAIRO-Theor. Inf. Appl. 42, 647-655 (2008)
DOI: 10.1051/ita:2008021

Comparing Complexity Functions of a Language and Its Extendable Part

Arseny M. Shur

Ural State University, Ekaterinburg, Russia; Arseny.Shur@usu.ru

Published online: 3 June 2008

Abstract
Right (left, two-sided) extendable part of a language consists of all words having infinitely many right (resp. left, two-sided) extensions within the language. We prove that for an arbitrary factorial language each of these parts has the same growth rate of complexity as the language itself. On the other hand, we exhibit a factorial language which grows superpolynomially, while its two-sided extendable part grows only linearly.

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