Array folds logic

P. Daca, T.A. Henzinger, A. Kupriyanov, in:, Springer, 2016, pp. 230–248.


Conference Paper | Published | English
Department
Series Title
LNCS
Abstract
We present an extension to the quantifier-free theory of integer arrays which allows us to express counting. The properties expressible in Array Folds Logic (AFL) include statements such as "the first array cell contains the array length," and "the array contains equally many minimal and maximal elements." These properties cannot be expressed in quantified fragments of the theory of arrays, nor in the theory of concatenation. Using reduction to counter machines, we show that the satisfiability problem of AFL is PSPACE-complete, and with a natural restriction the complexity decreases to NP. We also show that adding either universal quantifiers or concatenation leads to undecidability. AFL contains terms that fold a function over an array. We demonstrate that folding, a well-known concept from functional languages, allows us to concisely summarize loops that count over arrays, which occurs frequently in real-life programs. We provide a tool that can discharge proof obligations in AFL, and we demonstrate on practical examples that our decision procedure can solve a broad range of problems in symbolic testing and program verification.
Publishing Year
Date Published
2016-07-13
Volume
9780
Page
230 - 248
Conference
CAV: Computer Aided Verification
Conference Location
Toronto, Canada
Conference Date
2016-07-17 – 2016-07-23
IST-REx-ID

Cite this

Daca P, Henzinger TA, Kupriyanov A. Array folds logic. In: Vol 9780. Springer; 2016:230-248. doi:10.1007/978-3-319-41540-6_13
Daca, P., Henzinger, T. A., & Kupriyanov, A. (2016). Array folds logic (Vol. 9780, pp. 230–248). Presented at the CAV: Computer Aided Verification, Toronto, Canada: Springer. https://doi.org/10.1007/978-3-319-41540-6_13
Daca, Przemyslaw, Thomas A Henzinger, and Andrey Kupriyanov. “Array Folds Logic,” 9780:230–48. Springer, 2016. https://doi.org/10.1007/978-3-319-41540-6_13.
P. Daca, T. A. Henzinger, and A. Kupriyanov, “Array folds logic,” presented at the CAV: Computer Aided Verification, Toronto, Canada, 2016, vol. 9780, pp. 230–248.
Daca P, Henzinger TA, Kupriyanov A. 2016. Array folds logic. CAV: Computer Aided Verification, LNCS, vol. 9780. 230–248.
Daca, Przemyslaw, et al. Array Folds Logic. Vol. 9780, Springer, 2016, pp. 230–48, doi:10.1007/978-3-319-41540-6_13.

Link(s) to Main File(s)
Access Level
OA Open Access
Material in IST:
Dissertation containing IST record

Export

Marked Publications

Open Data IST Research Explorer

Search this title in

Google Scholar