PROJECTIONS OF SEMICOMPUTABLE RELATIONS ON ABSTRACT DATA TYPES

We consider projections of semicomputable relations on abstract structures We show that they arise in several contexts, including nondeterministic extensions of while programs with arrays by means of arbitrary initializations and random assignments. They form a basis for an investigation of the concept of algorithmic specifications of relations with nondeterministic search. An important technique in this investigation is the study of computation trees for imperative programs, in order to prove characterization theorems for semicomputable sets, of a form first developed by E. Engeler.