Abstract
Although every terminating loop has a ranking function, not every loop has a ranking function of a restricted form, such as a lexicographic tuple of polynomials over program variables. The polyranking principle is proposed as a generalization of polynomial ranking for analyzing termination of loops. We define lexicographic polyranking functions in the context of loops with parallel transitions consisting of polynomial assertions, including inequalities, over primed and unprimed variables. Next, we address synthesis of these functions with a complete and automatic method for synthesizing lexicographic linear polyranking functions with supporting linear invariants over linear loops.
This research was supported in part by NSF grants CCR-01-21403, CCR-02-20134, CCR-02-09237, CNS-0411363, and CCF-0430102, by ARO grant DAAD19-01-1-0723, and by NAVY/ONR contract N00014-03-1-0939. The first author was additionally supported by a Sang Samuel Wang Stanford Graduate Fellowship.
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Bradley, A.R., Manna, Z., Sipma, H.B. (2005). The Polyranking Principle. In: Caires, L., Italiano, G.F., Monteiro, L., Palamidessi, C., Yung, M. (eds) Automata, Languages and Programming. ICALP 2005. Lecture Notes in Computer Science, vol 3580. Springer, Berlin, Heidelberg. https://doi.org/10.1007/11523468_109
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DOI: https://doi.org/10.1007/11523468_109
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