Non-termination sets of simple linear loops

Authors:
Liyun Dai;Bican Xia
Affiliations:
LMAM & School of Mathematical Sciences, Peking University, China;LMAM & School of Mathematical Sciences, Peking University, China
Venue:
ICTAC'12 Proceedings of the 9th international conference on Theoretical Aspects of Computing
Year:
2012

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Abstract

A simple linear loop is a simple while loop with linear assignments and linear loop guards. If a simple linear loop has only two program variables, we give a complete algorithm for computing the set of all the inputs on which the loop does not terminate. For the case of more program variables, we show that the non-termination set cannot be described by Tarski formulae in general.