Elsevier

Theoretical Computer Science

Volume 131, Issue 2, 12 September 1994, Pages 311-330
Theoretical Computer Science

Language equations over a one-letter alphabet with union, concatenation and star: a complete solution

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Abstract

This paper develops a theory of language equations over a one-letter alphabet where the operations involved in the equations are union, unrestricted concatenation and star. Several key theorems are proven and tied together to provide an algorithm which enables one to solve any equation of this type. An application of this result is a constructive proof of the well-known fact that any context-free grammar with only one terminal always generates a regular language.

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Part of this research was carried out while the author was visiting the Universidade Federal do Rio Grande do Sul in Porto Alegre, Brazil; support through a grant from CNPq is acknowledged.