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 Diskr. Mat., 2011, Volume 23, Issue 1, Pages 72–83 (Mi dm1131)

A case of insolubility of the problem of equivalence of programs

V. L. Shcherbina

Abstract: 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.

DOI: https://doi.org/10.4213/dm1131

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English version:
Discrete Mathematics and Applications, 2011, 21:1, 131–144

Bibliographic databases:

UDC: 519.7

Citation: 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

Citation in format AMSBIB
\Bibitem{Shc11} \by V.~L.~Shcherbina \paper A case of insolubility of the problem of equivalence of programs \jour Diskr. Mat. \yr 2011 \vol 23 \issue 1 \pages 72--83 \mathnet{http://mi.mathnet.ru/dm1131} \crossref{https://doi.org/10.4213/dm1131} \mathscinet{http://www.ams.org/mathscinet-getitem?mr=2830698} \elib{http://elibrary.ru/item.asp?id=20730374} \transl \jour Discrete Math. Appl. \yr 2011 \vol 21 \issue 1 \pages 131--144 \crossref{https://doi.org/10.1515/DMA.2011.009} \scopus{http://www.scopus.com/record/display.url?origin=inward&eid=2-s2.0-79953298230}