Computer Science ›› 2017, Vol. 44 ›› Issue (1): 194-198, 213.doi: 10.11896/j.issn.1002-137X.2017.01.037

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New Method for Computing Eventual Linear Ranking Functions

ZHU Guang, LI Yi and WU Wen-yuan   

  • Online:2018-11-13 Published:2018-11-13

Abstract: Termination of linear loop programs has received extensive attention in these years.In this paper,we focused on the termination of linear constraint loops which has no traditional linear ranking functions.A method of detecting eventual linear ranking functions by Bagnara were introduced for termination analysis first.Such an eventual linear ranking function implies the loop terminates.We presented a new method for computing eventual linear ranking functions.Semi-algebraic systems,equivalent to linear increasing functions and eventual linear ranking functions,were established.Several methods for synthesizing eventual linear ranking functions were compared.And experimental results show that the semi-algebraic system for synthesis of eventual linear ranking functions established by our method is simpler.

Key words: Linear loop programs,Termination analysis,Eventual linear ranking functions,Mathematica

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