On Ianov's Program Schemata

Ianov has defined a formal abstraction of the notion of program which represents the sequential and control properties of a program but suppresses the details of the operations. For these schemata he defines a notion corresponding to computation and defines equivalence of schemata in terms of it. He then gives a decision procedure for equivalence of schemata, and a deductive formalism for generating schemata equivalent to a given one. The present paper is intended, first as an exposition of Ianov's results and simplification of his method, and second to point out certain generalizations and extensions of it. We define a somewhat generalized version of the notion of schema, in a language similar to that used in finite automata theory, and present a simple algorithm for the equivalence problem solved by Ianov. We also point out that the same problem for an extended notion of schema, considered rather briefly by Ianov, is just the equivalence problem for finite automata, which has been solved, although the decision procedure is rather long for practical use. A simple procedure for generating all schemata equivalent to a given schema is also indicated.