Analysis of Linear Definite Iterative Loops

Abstract

The paper presents a new method to prove the invariance of the system of linear inequalities and completability of linear definite iterative loops for imperative programs. Loop body is a linear operator that transforms the vector of program variables. The method takes into account loop precondition, as well as the condition of loop repetition in the form of a set of systems of linear inequalities. The method is based on the construction and analysis of the spectrum of linear operator and calculation of the number of loop iterations after which the invariance is either provided or disproved. The theory is illustrated by examples.