The undecidability of some equivalence problems concerning ngsm's and finite substitutions

Abstract

It is shown to be undecidable whether an ε-free finite substitution and a two-state simple ε-free ngsm are equivalent on ⇇b ∗ . Consequently, the state-minimization of such ngsm's and the nonterminal-minimization of linear grammars having two nonterminals are undecidable. Applications to some other decision problems concerning ε-free finite substitutions and linear grammars are also given. Finally it is shown that the time-equivalence problem is undecidable for propagating OL systems, i.e., for iterated ε-free finite substitutions. This solves an open problem presented in [4].