Infinite Loop Detection Based on Chains of Recurrence Algebra and Convergence of Iterative Sequence

Abstract

In this paper,two mathematical methods are proposed to detect the non-termination of two types of loop.The first method is based on chains of recurrence algebra.It is for detecting the non-termination of the loops in which the basic iterative relations of variables are linear or geometrical.All the variables in the loop are unified representation by the Chains of Recurrence Algebra(CR).Then the closed-form function of the loop condition about the number of loop iteration is deduced by the rules of CR.According to it the non-termination of loops can be decided through the monotonicity of the closed-form function and constraint solver.The second method is based on convergence of iterative sequence,which is for detecting the non-termination of the nonlinear loop.According to the convergence of iterative function and fixed-point we can determine the non-termination of the loops.In experiments,we analyzed 52loops which were presented by Velroyen[20]and 23loops which are from articles[18-19,21-23]and 13loops which are created by ourselves.The experimental results show that it can detect the non-termination of loop effectively.It can give the variable constraints which make the loop non-terminated.Meanwhile the number of loop iterations can be estimated when the loop is terminated.