On the equivalence of schemes

• Authors: Stephen J. Garland;David C. Luckham
• Venue: STOC '72 Proceedings of the fourth annual ACM symposium on Theory of computing
• Year: 1972

One objective of the study of schemes for computation is that of finding general methods for checking or verifying a given program against its specifications. If one views the program and its specification as presenting two supposedly equivalent schemes for a computation, then the objective reduces to one of finding general methods for determining whether, in fact, the two schemes are equivalent. Unfortunately, for many classes of schemes which are sufficiently powerful, this “equivalence problem” is not decidable, i.e. there are no general methods capable of determining, in all cases, whether two schemes in the class are equivalent. In this report we investigate the question of which classes of schemes have decidable equivalence problems, or, in otherwords the question of for which classes of schemes there exist general methods capable of determining equivalence.