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Complexity of Bradley-Manna-Sipma Lexicographic Ranking Functions

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Ben-Amran, Amir M., Amir M. and Genaim, Samir (2015) Complexity of Bradley-Manna-Sipma Lexicographic Ranking Functions. In 27th International Conference, CAV 2015, July 18-24, 2015, San Francisco (California).

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Official URL: http://link.springer.com/chapter/10.1007/978-3-319-21668-3_18#page-1



Abstract

In this paper we turn the spotlight on a class of lexicographic ranking functions introduced by Bradley, Manna and Sipma in a seminal CAV 2005 paper, and establish for the first time the complexity of some problems involving the inference of such functions for linear-constraint loops (without precondition). We show that finding such a function, if one exists, can be done in polynomial time in a way which is sound and complete when the variables range over the rationals (or reals). We show that when variables range over the integers, the problem is harder—deciding the existence of a ranking function is coNP-complete. Next, we study the problem of minimizing the number of components in the ranking function (a.k.a. the dimension). This number is interesting in contexts like computing iteration bounds and loop parallelization. Surprisingly, and unlike the situation for some other classes of lexicographic ranking functions, we find that even deciding whether a two-component ranking function exists is harder than the unrestricted problem: NP-complete over the rationals and Σ P 2 - complete over the integers.


Item Type:Conference or Workshop Item (Lecture)
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Publicado en Lecture Notes in Computer Science, vol. 9207

Subjects:Sciences > Computer science
Sciences > Computer science > Software
ID Code:37215
Deposited On:19 Apr 2016 15:48
Last Modified:20 Apr 2016 07:48

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