Termination of loop programs with polynomial guards

Authors:
Bin Wu;Liyong Shen;Zhongqin Bi;Zhenbing Zeng
Affiliations:
Shanghai Key Laboratory of Trustworthy Computing, East China Normal University, Shanghai, China;School of Mathematical Sciences, Graduate University of CAS, Beijing, China;Shanghai Key Laboratory of Trustworthy Computing, East China Normal University, Shanghai, China;Shanghai Key Laboratory of Trustworthy Computing, East China Normal University, Shanghai, China
Venue:
ICCSA'10 Proceedings of the 2010 international conference on Computational Science and Its Applications - Volume Part IV
Year:
2010

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Abstract

Termination analysis of loop programs is very important in many applications, especially in those of safety critical software. In this paper, the termination of programs with polynomial guards and linear assignments is simplified to decide solvability of semi-algebraic systems(SAS). If the number of functions are finite or the functions are integer periodic, then the termination of programs is decidable. The discussion is based on simplifying the linear loops by its Jordan form. And then the process to find the nonterminating points for general polynomial guards is proposed. For avoiding floating point computations in the process, a symbolic algorithm is given to compute the Jordan form of a matrix.