Two-dimensional finite state recognizability
Fundamenta Informaticae - Special issue on formal language theory
Handbook of formal languages, vol. 3
Regular binoid expressions and regular binoid languages
Theoretical Computer Science
Journal of Automata, Languages and Combinatorics
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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 @a=@b holds for all picture languages if and only if @a and @b 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.