A case of insolubility of the problem of equivalence of programs
V. L. Shcherbina
We consider algebraic models of sequential programs where the semantics of operators is defined on the base of a semigroup. In the paper, for the first time an example is constructed of a solvable semigroup with indecomposable neutral element for which the stopping problem for a Turing machine reduces to the problem of equivalence of programs over a given semigroup. All known examples of models of insoluble problem of equivalence of programs were based on groups. Thus, in the paper we succeeded in refining the boundary between soluble and insoluble cases of the problem of equivalence of programs in algebraic models. The obtained result supports also the importance of some sufficient conditions of solubility of the problem of equivalence of programs.
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Discrete Mathematics and Applications, 2011, 21:1, 131–144
V. L. Shcherbina, “A case of insolubility of the problem of equivalence of programs”, Diskr. Mat., 23:1 (2011), 72–83; Discrete Math. Appl., 21:1 (2011), 131–144
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\paper A case of insolubility of the problem of equivalence of programs
\jour Diskr. Mat.
\jour Discrete Math. Appl.
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