Abstract. The authors introduce the concept of eigenpolynomial of a linear operator, outline an algorithm to develop eigenpolynomials, and establish a relationship between eigenpolynomials and polynomial invariants of linear cycles of programs. The main result of the article is construction of a set of L-invariant cycles for operators with a Jordan form that contain nontrivial blocks. Refs: 15 titles.

Keywords: static program analysis, polynomial loops invariants, eigenpolynomials of linear operators, automatic generation problem.