ABC: Algebraic Bound Computation for loops

Blanc R, Henzinger TA, Hottelier T, Kovács L. 2010. ABC: Algebraic Bound Computation for loops. Logic for Programming, Artificial Intelligence, and Reasoning. LPAR: Conference on Logic for Programming, Artificial Intelligence and ReasoningLNCS vol. 6355, 103–118.


Conference Paper | Published | English

Scopus indexed
Author
Blanc, Régis; Henzinger, Thomas AISTA ; Hottelier, Thibaud; Kovács, Laura
Editor
Clarke, Edmund M; Voronkov, Andrei
Department
Abstract
We present ABC, a software tool for automatically computing symbolic upper bounds on the number of iterations of nested program loops. The system combines static analysis of programs with symbolic summation techniques to derive loop invariant relations between program variables. Iteration bounds are obtained from the inferred invariants, by replacing variables with bounds on their greatest values. We have successfully applied ABC to a large number of examples. The derived symbolic bounds express non-trivial polynomial relations over loop variables. We also report on results to automatically infer symbolic expressions over harmonic numbers as upper bounds on loop iteration counts.
Publishing Year
Date Published
2010-05-01
Proceedings Title
Logic for Programming, Artificial Intelligence, and Reasoning
Acknowledgement
This work was supported in part by the Swiss NSF. The fourth author is supported by an FWF Hertha Firnberg Research grant (T425-N23).
Volume
6355
Page
103-118
Conference
LPAR: Conference on Logic for Programming, Artificial Intelligence and Reasoning
Conference Location
Dakar, Senegal
Conference Date
2010-04-25 – 2010-05-01
ISSN
eISSN
IST-REx-ID

Cite this

Blanc R, Henzinger TA, Hottelier T, Kovács L. ABC: Algebraic Bound Computation for loops. In: Clarke EM, Voronkov A, eds. Logic for Programming, Artificial Intelligence, and Reasoning. Vol 6355. LNCS. Berlin, Heidelberg: Springer Nature; 2010:103-118. doi:10.1007/978-3-642-17511-4_7
Blanc, R., Henzinger, T. A., Hottelier, T., & Kovács, L. (2010). ABC: Algebraic Bound Computation for loops. In E. M. Clarke & A. Voronkov (Eds.), Logic for Programming, Artificial Intelligence, and Reasoning (Vol. 6355, pp. 103–118). Berlin, Heidelberg: Springer Nature. https://doi.org/10.1007/978-3-642-17511-4_7
Blanc, Régis, Thomas A Henzinger, Thibaud Hottelier, and Laura Kovács. “ABC: Algebraic Bound Computation for Loops.” In Logic for Programming, Artificial Intelligence, and Reasoning, edited by Edmund M Clarke and Andrei Voronkov, 6355:103–18. LNCS. Berlin, Heidelberg: Springer Nature, 2010. https://doi.org/10.1007/978-3-642-17511-4_7.
R. Blanc, T. A. Henzinger, T. Hottelier, and L. Kovács, “ABC: Algebraic Bound Computation for loops,” in Logic for Programming, Artificial Intelligence, and Reasoning, Dakar, Senegal, 2010, vol. 6355, pp. 103–118.
Blanc R, Henzinger TA, Hottelier T, Kovács L. 2010. ABC: Algebraic Bound Computation for loops. Logic for Programming, Artificial Intelligence, and Reasoning. LPAR: Conference on Logic for Programming, Artificial Intelligence and ReasoningLNCS vol. 6355, 103–118.
Blanc, Régis, et al. “ABC: Algebraic Bound Computation for Loops.” Logic for Programming, Artificial Intelligence, and Reasoning, edited by Edmund M Clarke and Andrei Voronkov, vol. 6355, Springer Nature, 2010, pp. 103–18, doi:10.1007/978-3-642-17511-4_7.
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