A note on identities of two-dimensional languages

Authors:
Igor Dolinka
Affiliations:
Department of Mathematics and Informatics, University of Novi Sad, Trg Dositeja Obradovića 4, 21000 Novi Sad, Serbia and Montenegro
Venue:
Discrete Applied Mathematics
Year:
2005

Citing 4
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Abstract

In this note we consider identical laws satisfied by two-dimensional (picture) languages, collections of rectangular arrays over a given alphabet. We prove that an identity α = β holds for all picture languages if and only if α and β represent the same bi-language (a subset of a free bi-monoid). As a consequence, we obtain decidability of the equational theory of picture languages, a description of free objects in the variety generated by picture language algebras, and prove that such a variety does not have a finite equational axiomatization.