A case of insolubility of the problem of equivalence of programs
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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.
© de Gruyter 2011
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Artikel in diesem Heft
- On the maximum size of a tree in a random unlabelled unrooted forest
- Asymptotic normality of the number of values of m-dependent random variables which occur a given number of times
- Limit theorems for the joint distribution of component sizes of a random mapping with a known number of components
- A combinatorial approach to calculation of moments of characteristics of runs in ternary Markov sequences
- The critical ω-foliated τ-closed formations of finite groups
- On the semigroups of endomorphisms of direct products of commutative Moufang loops
- The Voronoi polyhedra of the rooted lattice E6 and of its dual lattice
- Calculation of the characteristic polynomial of a matrix
- A case of insolubility of the problem of equivalence of programs
