EXTENDING REGULAR EXPRESSIONSWITH HOMOMORPHIC REPLACEMENT,

We define H- and EH-expressions as extensions of regularexpressions by adding homomorphic and iterated homomorphicreplacement as new operations, resp. The definition is analogous tothe extension given by Gruska in order to characterize context-freelanguages. We compare the families of languages obtained by these extensionswith the families of regular, linear context-free, context-free,and EDT0L languages. Moreover, relations to language families basedon patterns, multi-patterns, pattern expressions, H-systems and uniformsubstitutions are also investigated. Furthermore, we present theirclosure properties with respect to TRIO operations and discuss thedecidability status and complexity of fixed and general membership,emptiness, and the equivalence problem