A direct branching algorithm for checking equivalence of some classes of deterministic pushdown automata

A new direct algorithm is presented for checking equivalence of some classes of deterministic pushdown automata (dpda's), after Korenjak and Hopcroft's branching algorithm. It is not only powerful enough to be applicable to two dpda's accepting by empty stack, one of which is real-time, but also simple even for dpda's in lower subclasses. This is the first time the branching algorithm has been used to give such a general decision procedure without ever “mixing” the two languages in question. In other words, it deals with only the equivalence equation whose left-hand side consists of a pure reachable configuration of one dpda and whose right-hand side that of the other