Machine Characterization of (E0L-E0L) Array Languages

A traditional topic in formal language theory, is to characterize classes of languages by machine models. Extending the idea of machine characterization of L systems to two dimensions and at the same time to generate pictures which are not rectangular, we propose in this paper a new model called (E0L-E0L) array system. (E0L-E0L) array languages are obtained by substituting E0L languages vertically into E0L languages. First a horizontal line of intermediates is generated by an E0L system. Then E0L languages are substituted vertically for each intermediate cell resulting in a two-dimensional language which need not be rectangular. We propose in this paper (Restricted Pushdown Array of Counters-Restricted Pushdown Array of Counters) array automata ((RPAC-RPAC)AA) and we show that a language is a (RPAC-RPAC)AA language if and only if it is a (E0L-E0L)A language.