The Equivalence Problem for LL - and L / ? - Regular Grammars

The equivalence problem for context-free grammars is “given two arbitrary grammars, do they generate the same language ?” Since this is undecidable in general attention has been restricted to decidable subclasses of the context-free grammars. For example, the classes of U(k) grammars and real-time strict deterministic grammars. In this paper it is shown that the equivalence problem for U-regular grammars is decidable by reducing it to the equivalence problem for real-time strict deterministic grammars. Moreover, we show that the U-regular equivalence problem is a special case of a more general equivalence problem which is also decidable. Our techniques can also be used to show that the equivalence problem for LR-regular grammars is decidable if and only if the equivalence problem for U?(O) grammars is decidable.