Theory of recursive functions and effective computability
Theory of recursive functions and effective computability
Journal of the ACM (JACM)
Random-Access Stored-Program Machines, an Approach to Programming Languages
Journal of the ACM (JACM)
The Equivalence Problem of Simple Programs
Journal of the ACM (JACM)
The complexity of loop programs
ACM '67 Proceedings of the 1967 22nd national conference
Computation: finite and infinite machines
Computation: finite and infinite machines
Formal languages and their relation to automata
Formal languages and their relation to automata
Simple deterministic languages
SWAT '66 Proceedings of the 7th Annual Symposium on Switching and Automata Theory (swat 1966)
On formalised computer programs
Journal of Computer and System Sciences
The Equivalence Problem for Computational Models: Decidable and Undecidable Cases
MCU '01 Proceedings of the Third International Conference on Machines, Computations, and Universality
Deterministic one-counter automata
Journal of Computer and System Sciences
Program equivalence checking by two-tape automata
Cybernetics and Systems Analysis
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Some of the assertions about programs which we might be interested in proving are concerned with correctness, equivalence, accessibility of subroutines and guarantees of termination. We should like to develop techniques for determining such properties efficiently and intelligently wherever possible. Though theory tells us that for a realistic programming language almost any interesting property of the behaviour is effectively undecidable, this situation may not be intolerable in practice. An unsolvability result just gives us warning that we may not be able to solve all of the problems we are presented with, and that some of the ones we can solve will be very hard. In such circumstances it is very reasonable to try and determine necessary or sufficient conditions on programs for our techniques to be assured of success; however, in this paper we shall discuss a more qualitative, indirect, approach. We consider a range of more or less simplified computer models, chosen judiciously to exemplify some particular feature or features of computation. A demonstration of unsolvability in such a model reveals more accurately those sources which can contribute to unsolvability in a more complicated structure. On the other hand a decision procedure may illustrate a technique of practical use. It is our thesis that this kind of strategy of exploration can and will yield insight and practical advances in the theory of computation. Provided that the model retains some practical relevance, the dividends are the greater the nearer the decision problem lies to the frontier between solvability and unsolvability.