Pattern Language Recognition and Generation

A k-bounded recognizable pattern language is the set of all k-bounded patterns that are obtained as behaviors of a pattern automaton. The emptiness and the equality problems for k-bounded behaviors of pattern automata are proved to be decidable. Moreover, we examine their relationship with context free pattern grammars, which are basically the hyperedge replacement grammars on planar directed acyclic graphs. An important result is that the classes of k-bounded recognizable and context free pattern languages are cones with respect to (k-bounded) pattern transductions. Pattern automata are also used to study 0-type grammars and word rewriting systems. It is proved that the emptiness problem is decidable for the set of k-bounded derivations of a 0-type grammar and that k-bounded confluence and k-bounded termination are decidable for word rewriting systems.