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.
This is a preview of subscription content, log in via an institution to check access.
Preview
Unable to display preview. Download preview PDF.
Similar content being viewed by others
References
Bradley, A.R., Manna, Z., Sipma, H.B.: Linear ranking with reachability. In: Etessami, K., Rajamani, S.K. (eds.) CAV 2005. LNCS, vol. 3576, pp. 491–504. Springer, Heidelberg (2005)
Bradley, A.R., Manna, Z., Sipma, H.B.: Termination of polynomial programs. In: Cousot, R. (ed.) VMCAI 2005. LNCS, vol. 3385, pp. 113–129. Springer, Heidelberg (2005)
Codish, M., Genaim, S., Bruynooghe, M., Gallagher, J., Vanhoof, W.: One lop at a time. In: WST (2003)
Colón, M., Sipma, H.B.: Synthesis of linear ranking functions. In: Margaria, T., Yi, W. (eds.) TACAS 2001. LNCS, vol. 2031, pp. 67–81. Springer, Heidelberg (2001)
Colón, M.A., Sipma, H.B.: Practical methods for proving program termination. In: Brinksma, E., Larsen, K.G. (eds.) CAV 2002. LNCS, vol. 2404, pp. 442–454. Springer, Heidelberg (2002)
Cousot, P.: Proving program invariance and termination by parametric abstraction, lagrangian relaxation and semidefinite programming. In: Cousot, R. (ed.) VMCAI 2005. LNCS, vol. 3385, pp. 1–24. Springer, Heidelberg (2005)
Dershowitz, N., Lindenstrauss, N., Sagiv, Y., Serebrenik, A.: A general framework for automatic termination analysis of logic programs. Applicable Algebra in Engineering, Communication and Computing 12, 117–156 (2001)
Lee, C.S., Jones, N.D., Ben-Amram, A.M.: The size-change principle for program termination. In: POPL, pp. 81–92 (2001)
Manna, Z., Browne, A., Sipma, H.B., Uribe, T.E.: Visual abstractions for temporal verification. Algebraic Methodology and Software Technology, 28–41 (1998)
Podelski, A., Rybalchenko, A.: A complete method for the synthesis of linear ranking functions. In: Steffen, B., Levi, G. (eds.) VMCAI 2004. LNCS, vol. 2937, pp. 239–251. Springer, Heidelberg (2004)
Podelski, A., Rybalchenko, A.: Transition invariants. In: LICS, pp. 32–41 (2004)
Schrijver, A.: Theory of Linear and Integer Programming. Wiley, Chichester (1986)
Sipma, H.B., Uribe, T.E., Manna, Z.: Deductive model checking. In: CAV, pp. 209–219 (1996)
Tiwari, A.: Termination of linear programs. In: Alur, R., Peled, D.A. (eds.) CAV 2004. LNCS, vol. 3114, pp. 70–82. Springer, Heidelberg (2004)
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2005 Springer-Verlag Berlin Heidelberg
About this paper
Cite this paper
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
Download citation
DOI: https://doi.org/10.1007/11523468_109
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-27580-0
Online ISBN: 978-3-540-31691-6
eBook Packages: Computer ScienceComputer Science (R0)