This article is cited in 1 paper

On complexity of solving systems of functional equations in countable-valued logic

S. S. Marchenkov

Moscow State University, 1 Leninskie gory, 119991 Moscow, Russia

Abstract: We propose a procedure to construct all solutions of an arbitrary system of functional equations in countable-valued logic. Based on this procedure, the solutions of systems of equations in the class $\Sigma_2$ of Kleene–Mostovsky arithmetical hierarchy which include only the ternary discriminator $p$ are determined. We prove that for given systems of equations the components of solutions may be arbitrary functions of the class $\Sigma^1_1$ of Kleene analytical hierarchy. Bibliogr. 10.

Keywords: system of functional equations, function of countable-valued logic.

UDC: 519.716

Received: 02.09.2014
Revised: 25.01.2015

DOI: 10.17377/daio.2015.22.460

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