A Recursion Theoretic Approach to Program Testing

Inductive inference, the automatic synthesis of programs, bears certain ostensible relationships with program testing. For inductive inference, one must take a finite sample of the desired input/output behavior of some program and produce (synthesize) an equivalent program. In the testing paradigm, one seeks a finite sample for a function such that any program (in a given set) which computes something other than the object function differs from the object function on the finite sample. In both cases, the finite sample embodies sufficient knowledge to isolate the desired program from all other possibilities. These relationships are investigated and general recursion theoretic properties of testable sets of functions are exposed.