Regular Expressions and the Equivalence of Programs

If we assume that the study and detection of equivalence for ALGOLl ike programs holds certain pragmatic interest, then it seems reasonable to pursue these matters despite the well-known undecidability of this property. Various efforts have been made to isolate decidable sub-cases of this equivalence problem (e.g., by Paterson [12] and this author [6]). Other efforts have been made to define weaker, and therefore decidable, sorts of equivalence (e.g., by Ianov [4] and Rutledge [14]). Our interest here is to develop equivalence detecting procedures applicable to programs for which equivalence is undecidable. These procedures always produce an answer when questioned as to the equivalence of two programs: either YES or MAYBE. We consider a sequence of these procedures, each more powerful than the preceding ones. Thus, if one procedure returns MAYBE, then perhaps a subsequent more powerful one will return YEs.