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2016 | OriginalPaper | Chapter

PTIME Computation of Transitive Closures of Octagonal Relations

Author : Filip Konečný

Published in: Tools and Algorithms for the Construction and Analysis of Systems

Publisher: Springer Berlin Heidelberg

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Abstract

Computing transitive closures of integer relations is the key to finding precise invariants of integer programs. In this paper, we study difference bounds and octagonal relations and prove that their transitive closure is a PTIME-computable formula in the existential fragment of Presburger arithmetic. This result marks a significant complexity improvement, as the known algorithms have EXPTIME worst case complexity.

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previous chapter Interpolants in Nonlinear Theories Over the Reals
next chapter Scalable Verification of Linear Controller Software
Footnotes
1
Quantifier-Free Presburger Arithmetic.
 
Literature
1.
Bozga, M., Gîrlea, C., Iosif, R.: Iterating octagons. In: Kowalewski, S., Philippou, A. (eds.) TACAS 2009. LNCS, vol. 5505, pp. 337–351. Springer, Heidelberg (2009)CrossRef
2.
Bozga, M., Iosif, R., Konečný, F.: Fast acceleration of ultimately periodic relations. In: Touili, T., Cook, B., Jackson, P. (eds.) CAV 2010. LNCS, vol. 6174, pp. 227–242. Springer, Heidelberg (2010)CrossRef
3.
Bozga, M., Iosif, R., Konečný, F.: The complexity of reachability problems for flat counter machines with periodic loops. Technical Report (2013). arXiv.​5321 (1307)
4.
Bozga, M., Iosif, R., Konečný, F.: Deciding conditional termination. Log. Meth. Comput. Sci. 10(3) (2014)
5.
Bozga, M., Iosif, R., Konečný, F.: Safety problems are NP-complete for flat integer programs with octagonal loops. In: McMillan, K.L., Rival, X. (eds.) VMCAI 2014. LNCS, vol. 8318, pp. 242–261. Springer, Heidelberg (2014)CrossRef
6.
Bozga, M., Iosif, R., Lakhnech, Y.: Flat parametric counter automata. Fundamenta Informaticae 91(2), 275–303 (2009)MathSciNetMATH
7.
Comon, H., Jurski, Y.: Multiple counters automata, safety analysis and presburger arithmetic. In: Hu, A.J., Vardi, M.Y. (eds.) Proceedings of CAV. LNCS, vol. 1427, pp. 268–279. Springer, Heidelberg (1998)
8.
Hojjat, H., Iosif, R., Konečný, F., Kuncak, V., Rümmer, P.: Accelerating interpolants. In: Chakraborty, S., Mukund, M. (eds.) ATVA 2012. LNCS, vol. 7561, pp. 187–202. Springer, Heidelberg (2012)CrossRef
9.
Hojjat, H., Konečný, F., Garnier, F., Iosif, R., Kuncak, V., Rümmer, P.: A verification toolkit for numerical transition systems - tool paper. In: Proceedings of FM, pp. 247–251 (2012)
10.
Miné, A.: Weakly Relational Numerical Abstract Domains (2004)
11.
12.
Wang, C., Ivančić, F., Ganai, M.K., Gupta, A.: Deciding separation logic formulae by SAT and incremental negative cycle elimination. In: Sutcliffe, G., Voronkov, A. (eds.) LPAR 2005. LNCS (LNAI), vol. 3835, pp. 322–336. Springer, Heidelberg (2005)CrossRef
Metadata
Title
PTIME Computation of Transitive Closures of Octagonal Relations
Author
Filip Konečný
Copyright Year
2016
Publisher
Springer Berlin Heidelberg
Book
Tools and Algorithms for the Construction and Analysis of Systems

Print ISBN: 978-3-662-49673-2

Electronic ISBN: 978-3-662-49674-9

Copyright Year: 2016

DOI
https://doi.org/10.1007/978-3-662-49674-9_42

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