A note on identities of two-dimensional languages

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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.

Keywords

Two-dimensional (picture) language
Bi-language
Equational theory
Free algebra

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Supported by Grant No.1227 of the Ministry of Science and Environment of Republic of Serbia.