Abstract
We consider the problem of defining regular expressions to characterize the class of recognizable picture languages in the case of a one-letter alphabet. We define a diagonal concatenation and its star and consider two different families, L ( D ) and L ( \CRD\ ) , of languages denoted by regular expressions involving such operations plus classical operations. L ( D ) is characterized both in terms of rational relations and in terms of two-dimensional automata moving only right and down. L ( \CRD\ ) is included in \REC\ and contains languages defined by three-way automata while languages in L ( \CRD\ ) necessarily satisfy some regularity conditions. Finally, we introduce new definitions of advanced stars expressing the necessity of conceptually different definitions for iteration.
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