This paper investigates the termination problems of multi-path polynomial programs （MPPs） with equational loop guards. To establish sufficient conditions for termination and nontermination simultaneously, the author...This paper investigates the termination problems of multi-path polynomial programs （MPPs） with equational loop guards. To establish sufficient conditions for termination and nontermination simultaneously, the authors propose the notion of strong/weak non-termination which under/over- approximates non-termination. Based on polynomial ideal theory, the authors show that the set of all strong non-terminating inputs （SNTI） and weak non-terminating inputs （WNTI） both correspond to tile real varieties of certain polynomial ideals. Furthermore, the authors prove that the variety of SNTI is computable, and under some sufficient conditions the variety of WNTI is also computable. Then by checking the computed SNTI and WNTI varieties in parallel, termination properties of a consid- ered MPP can be asserted. As a consequence, the authors establish a new framework for termination analysis of MPPs.展开更多
基金supported by the National Basic Research Program of China under Grant No.2014CB340700the National Science and Technology Major Project of China under Grant No.2012ZX01039-004+3 种基金the National Natural Science Foundation of China under Grant Nos.91118007,11071273,61202131,11401218,cstc2012ggB40004,cstc2013jjys40001SRFDP under Grant No.20130076120010the Open Project of Shanghai Key Laboratory of Trustworthy Computing under Grant No.07dz22304201307West Light Foundation of Chinese Academy of Sciences
文摘This paper investigates the termination problems of multi-path polynomial programs （MPPs） with equational loop guards. To establish sufficient conditions for termination and nontermination simultaneously, the authors propose the notion of strong/weak non-termination which under/over- approximates non-termination. Based on polynomial ideal theory, the authors show that the set of all strong non-terminating inputs （SNTI） and weak non-terminating inputs （WNTI） both correspond to tile real varieties of certain polynomial ideals. Furthermore, the authors prove that the variety of SNTI is computable, and under some sufficient conditions the variety of WNTI is also computable. Then by checking the computed SNTI and WNTI varieties in parallel, termination properties of a consid- ered MPP can be asserted. As a consequence, the authors establish a new framework for termination analysis of MPPs.
