Program equivalence and context-free grammars

Abstract

This note defines a new equivalence relation among systems of recursion equations and a method for assigning context-free grammars to these systems, such that (1) The new equivalence implies strong equivalence; (2) Systems are equivalent in the new sense iff their grammars generate the same language; (3) There is a nontrivial decidable class of systems whose grammars have the decidability properties of LL(k) grammars. Thus, the decidability of generative equivalence for LL(k) grammars mitigates the general undecidability of strong equivalence between arbitrary systems of recursion equations.