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The Structure of Polynomial Invariants of Linear Loops

  • Software–Hardware Systems
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Cybernetics and Systems Analysis Aims and scope

Abstract

. This article considers the problem of generating polynomial invariants for iterative loops with loop initialization statements and nonsingular linear operators in loop bodies. The set of such invariants forms an ideal in the ring of polynomials in the loop variables. Two algorithms are presented one of which calculates basic invariants for a linear operator in the form of a Jordan cell and the other calculates basic invariants for a diagonalizable linear operator with an irreducible minimal characteristic polynomial. The following theorem on the structure of the basis of the ideal of invariants for such an operator is proved: this basis consists of basic invariants of Jordan cells and basic invariants of the diagonalizable part of the linear operator being considered.

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Authors and Affiliations

  1. Kherson State University, Kherson, Ukraine

    M. S. Lvov

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  1. M. S. Lvov
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Correspondence to M. S. Lvov.

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Translated from Kibernetika i Sistemnyi Analiz, No. 3, pp. 143–156, May–June, 2015. Original article submitted March 17, 2014.

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Lvov, M.S. The Structure of Polynomial Invariants of Linear Loops. Cybern Syst Anal 51, 448–460 (2015). https://doi.org/10.1007/s10559-015-9736-7

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  • DOI: https://doi.org/10.1007/s10559-015-9736-7

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