Definability in the Existential Theory of Concatenation and Undecidable Extensions of this Theory

Abstract

We study extensions of the decidable existential theory of concatenation over words. We show that two equal-length predicates are equivalent and are not existentially definable by equations in concatenation. By adding a further length predicate we get an undecidable existential theory. Whether the existential theory of concatenation and equal length is decidable remains unknown.

The results in this paper are contained in the Ph. d. thesis [6] of the second author written under the direction of the first author. Professor Büchi died in April 1984.