The Decision Problem for Effective Procedures

Abstract The “somewhat vague, intuitive” notion from computability theory of an effective procedure (method) or algorithm can be fairly precisely defined even if it is not sufficiently formal and precise to belong mathematics proper (in a narrow sense)—and (as many have asserted) for that reason the Church–Turing thesis unprovable. It proved logically class procedures decidable, i.e., there no ascertaining whether given effective. This result directly itself procedure, without reliance on any (partly) mathematical lemma, conjecture, invoking recursiveness Turing-computability. In fact, anything very mathematical. proof does appeal definition ‘effective procedure’. Instead, relies solely entirely basic grasp intuitive procedure. Though effectiveness undecidable surprising, also significance. has consequence, example, solution decision problem, complete, must accompanied by separate argument proposed ascertainment invariably terminates with correct verdict.