caa a22 4500 605518882 CHVBK 20210128100727.0 cr unu---uuuuu 210128e20150501xx s 000 0 eng 10.1007/s10559-015-9736-7 doi (NATIONALLICENCE)springer-10.1007/s10559-015-9736-7 Lvov M. Kherson State University, Kherson, Ukraine aut The Structure of Polynomial Invariants of Linear Loops [Elektronische Daten] [M. Lvov] . 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. Springer Science+Business Media New York, 2015 static analysis of programs nationallicence linear loop nationallicence loop invariant nationallicence invariant polynomial nationallicence Cybernetics and Systems Analysis Springer US; http://www.springer-ny.com 51/3(2015-05-01), 448-460 1060-0396 51:3<448 2015 51 10559 https://doi.org/10.1007/s10559-015-9736-7 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s10559-015-9736-7 text/html Onlinezugriff via DOI NATIONALLICENCE 100 1- Lvov M. Kherson State University, Kherson, Ukraine aut NATIONALLICENCE 773 0- Cybernetics and Systems Analysis Springer US; http://www.springer-ny.com 51/3(2015-05-01), 448-460 1060-0396 51:3<448 2015 51 10559