Article

Termination analysis with compositional transition invariants

Authors:

Daniel Kroening,

Natasha Sharygina,

Aliaksei Tsitovich,

Christoph M. WintersteigerAuthors Info & Claims

CAV'10: Proceedings of the 22nd international conference on Computer Aided Verification

Pages 89 - 103

https://doi.org/10.1007/978-3-642-14295-6_9

Published: 15 July 2010 Publication History

Abstract

Modern termination provers rely on a safety checker to construct disjunctively well-founded transition invariants This safety check is known to be the bottleneck of the procedure We present an alternative algorithm that uses a light-weight check based on transitivity of ranking relations to prove program termination We provide an experimental evaluation over a set of 87 Windows drivers, and demonstrate that our algorithm is often able to conclude termination by examining only a small fraction of the program As a consequence, our algorithm is able to outperform known approaches by multiple orders of magnitude.

References

[1]

Cook, B., Podelski, A., Rybalchenko, A.: Termination proofs for systems code In: PLDI, pp 415-426 ACM, New York (2006)

Digital Library

[2]

Cook, B., Kroening, D., Ruemmer, P., Wintersteiger, C.: Ranking function synthesis for bit-vector relations In: TACAS, pp 236-250 Springer, Heidelberg (2010)

Digital Library

[3]

Podelski, A., Rybalchenko, A.: Transition invariants In: LICS, pp 32-41 IEEE Computer Society, Los Alamitos (2004)

Digital Library

[4]

Colón, M., Sipma, H.: Synthesis of linear ranking functions In: Margaria, T., Yi, W (eds.) TACAS 2001 LNCS, vol 2031, pp 67-81 Springer, Heidelberg (2001)

Digital Library

[5]

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 465-486 Springer, Heidelberg (2004)

[6]

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)

Digital Library

[7]

Podelski, A., Rybalchenko, A.: ARMC: The logical choice for software model checking with abstraction refinement In: Hanus, M (ed.) PADL 2007 LNCS, vol 4354, pp 245-259 Springer, Heidelberg (2006)

Digital Library

[8]

Horwitz, S., Reps, T.W., Binkley, D.: Interprocedural slicing using dependence graphs In: PLDI, pp 35-46 ACM, New York (1988)

Digital Library

[9]

Kroening, D., Sharygina, N., Tonetta, S., Tsitovich, A., Wintersteiger, C.M.: Loop summarization using abstract transformers In: Cha, S(S.), Choi, J.-Y., Kim, M., Lee, I., Viswanathan, M (eds.) ATVA 2008 LNCS, vol 5311, pp 111-125 Springer, Heidelberg (2008)

Digital Library

[10]

Clarke, E., Kroening, D., Lerda, F.: A tool for checking ANSI-C programs In: Jensen, K., Podelski, A (eds.) TACAS 2004 LNCS, vol 2988, pp 168-176 Springer, Heidelberg (2004)

[11]

Cook, B., Gulwani, S., Lev-Ami, T., Rybalchenko, A., Sagiv, M.: Proving conditional termination In: Gupta, A., Malik, S (eds.) CAV 2008 LNCS, vol 5123, pp 328-340 Springer, Heidelberg (2008)

Digital Library

[12]

Turing, A.M.: On computable numbers, with an application to the Entscheidungsproblem Proc London Math Soc 2, 230-265 (1936)

[13]

Turing, A.: Checking a large routine In: Report of a Conference on High Speed Automatic Calculating Machines, Univ Math Lab., Cambridge, pp 67-69 (1949)

[14]

Codish, M., Taboch, C.: A semantic basis for termination analysis of logic programs and its realization using symbolic norm constraints In: Hanus, M., Heering, J., Meinke, K (eds.) ALP 1997 and HOA 1997 LNCS, vol 1298, pp 31-45 Springer, Heidelberg (1997)

Digital Library

[15]

Thiemann, R., Giesl, J.: The size-change principle and dependency pairs for termination of term rewriting Appl Alg in Eng., Comm & Comp 16, 229-270 (2005)

[16]

Lee, C.S., Jones, N.D., Ben-Amram, A.M.: The size-change principle for program termination In: POPL, pp 81-92 ACM, New York (2001)

Digital Library

[17]

Colón, M., Sipma, H.: Practical methods for proving program termination In: Brinksma, E., Larsen, K.G (eds.) CAV 2002 LNCS, vol 2404, pp 442-454 Springer, Heidelberg (2002)

Digital Library

[18]

Cook, B., Podelski, A., Rybalchenko, A.: Abstraction refinement for termination In: Hankin, C., Siveroni, I (eds.) SAS 2005 LNCS, vol 3672, pp 87-101 Springer, Heidelberg (2005)

Digital Library

[19]

Berdine, J., Chawdhary, A., Cook, B., Distefano, D., O'Hearn, P.: Variance analyses from invariance analyses SIGPLAN Not 42, 211-224 (2007)

Digital Library

[20]

Biere, A., Artho, C., Schuppan, V.: Liveness checking as safety checking Electr Notes Theor Comput Sci 66 (2002)

Cited By

Raad AVanegue JO’Hearn P(2024)Non-termination Proving at ScaleProceedings of the ACM on Programming Languages10.1145/36897208:OOPSLA2(246-274)Online publication date: 8-Oct-2024
https://dl.acm.org/doi/10.1145/3689720
Alon YDavid CRoychoudhury ACadar CKim M(2022)Using graph neural networks for program terminationProceedings of the 30th ACM Joint European Software Engineering Conference and Symposium on the Foundations of Software Engineering10.1145/3540250.3549095(910-921)Online publication date: 7-Nov-2022
https://dl.acm.org/doi/10.1145/3540250.3549095
Xu RChen JHe FDwyer MDamian DZeller A(2022)Data-driven loop bound learning for termination analysisProceedings of the 44th International Conference on Software Engineering10.1145/3510003.3510220(499-510)Online publication date: 21-May-2022
https://dl.acm.org/doi/10.1145/3510003.3510220
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Termination analysis with compositional transition invariants

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Information & Contributors

Information

Published In

cover image Guide Proceedings

CAV'10: Proceedings of the 22nd international conference on Computer Aided Verification

July 2010

673 pages

ISBN:364214294X

Editors:
Tayssir Touili
LIAFA, CNRS and University Paris Diderot, Paris Cedex 13, France
,
Byron Cook
LIAFA, Microsoft Research, Roger Needham Building, J J Thomson Avenue, Cambridge, UK
,
Paul Jackson
School of Informatics, University of Edinburgh, Roger Needham Building, J J Thomson Avenue, Edinburgh, UK

Sponsors

EPSRC: Engineering and Physical Sciences Research Council
NEC
Jasper Design Automation: Jasper Design Automation
IBMR: IBM Research
Microsoft Research: Microsoft Research

Publisher

Springer-Verlag

Berlin, Heidelberg

Publication History

Published: 15 July 2010

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Cited By

Raad AVanegue JO’Hearn P(2024)Non-termination Proving at ScaleProceedings of the ACM on Programming Languages10.1145/36897208:OOPSLA2(246-274)Online publication date: 8-Oct-2024
https://dl.acm.org/doi/10.1145/3689720
Alon YDavid CRoychoudhury ACadar CKim M(2022)Using graph neural networks for program terminationProceedings of the 30th ACM Joint European Software Engineering Conference and Symposium on the Foundations of Software Engineering10.1145/3540250.3549095(910-921)Online publication date: 7-Nov-2022
https://dl.acm.org/doi/10.1145/3540250.3549095
Xu RChen JHe FDwyer MDamian DZeller A(2022)Data-driven loop bound learning for termination analysisProceedings of the 44th International Conference on Software Engineering10.1145/3510003.3510220(499-510)Online publication date: 21-May-2022
https://dl.acm.org/doi/10.1145/3510003.3510220
He FHan J(2020)Termination analysis for evolving programs: an incremental approach by reusing certified modulesProceedings of the ACM on Programming Languages10.1145/34282674:OOPSLA(1-27)Online publication date: 13-Nov-2020
https://dl.acm.org/doi/10.1145/3428267
Chen YHeizmann MLengál OLi YTsai MTurrini AZhang L(2018)Advanced automata-based algorithms for program termination checkingACM SIGPLAN Notices10.1145/3296979.319240553:4(135-150)Online publication date: 11-Jun-2018
https://dl.acm.org/doi/10.1145/3296979.3192405
Chen YHeizmann MLengál OLi YTsai MTurrini AZhang LFoster JGrossman D(2018)Advanced automata-based algorithms for program termination checkingProceedings of the 39th ACM SIGPLAN Conference on Programming Language Design and Implementation10.1145/3192366.3192405(135-150)Online publication date: 11-Jun-2018
https://dl.acm.org/doi/10.1145/3192366.3192405
David CKesseli PKroening DLewis M(2018)Program Synthesis for Program AnalysisACM Transactions on Programming Languages and Systems10.1145/317480240:2(1-45)Online publication date: 28-May-2018
https://dl.acm.org/doi/10.1145/3174802
Agrawal SChatterjee KNovotný P(2017)Lexicographic ranking supermartingales: an efficient approach to termination of probabilistic programsProceedings of the ACM on Programming Languages10.1145/31581222:POPL(1-32)Online publication date: 27-Dec-2017
https://dl.acm.org/doi/10.1145/3158122
Padon OHoenicke JLosa GPodelski ASagiv MShoham S(2017)Reducing liveness to safety in first-order logicProceedings of the ACM on Programming Languages10.1145/31581142:POPL(1-33)Online publication date: 27-Dec-2017
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Chen HDavid CKroening DSchrammel PWachter B(2017)Bit-Precise Procedure-Modular Termination AnalysisACM Transactions on Programming Languages and Systems10.1145/312113640:1(1-38)Online publication date: 10-Dec-2017
https://dl.acm.org/doi/10.1145/3121136
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