--- _id: '1391' abstract: - lang: eng text: "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.\r\nAFL 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." alternative_title: - LNCS author: - first_name: Przemyslaw full_name: Daca, Przemyslaw id: 49351290-F248-11E8-B48F-1D18A9856A87 last_name: Daca - first_name: Thomas A full_name: Henzinger, Thomas A id: 40876CD8-F248-11E8-B48F-1D18A9856A87 last_name: Henzinger orcid: 0000−0002−2985−7724 - first_name: Andrey full_name: Kupriyanov, Andrey id: 2C311BF8-F248-11E8-B48F-1D18A9856A87 last_name: Kupriyanov citation: ama: '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' apa: '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' chicago: 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. ieee: '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.' ista: 'Daca P, Henzinger TA, Kupriyanov A. 2016. Array folds logic. CAV: Computer Aided Verification, LNCS, vol. 9780, 230–248.' mla: Daca, Przemyslaw, et al. Array Folds Logic. Vol. 9780, Springer, 2016, pp. 230–48, doi:10.1007/978-3-319-41540-6_13. short: P. Daca, T.A. Henzinger, A. Kupriyanov, in:, Springer, 2016, pp. 230–248. conference: end_date: 2016-07-23 location: Toronto, Canada name: 'CAV: Computer Aided Verification' start_date: 2016-07-17 date_created: 2018-12-11T11:51:45Z date_published: 2016-07-13T00:00:00Z date_updated: 2023-09-07T11:58:33Z day: '13' department: - _id: ToHe doi: 10.1007/978-3-319-41540-6_13 ec_funded: 1 intvolume: ' 9780' language: - iso: eng main_file_link: - open_access: '1' url: http://arxiv.org/abs/1603.06850 month: '07' oa: 1 oa_version: Preprint page: 230 - 248 project: - _id: 25EE3708-B435-11E9-9278-68D0E5697425 call_identifier: FP7 grant_number: '267989' name: Quantitative Reactive Modeling - _id: 25832EC2-B435-11E9-9278-68D0E5697425 call_identifier: FWF grant_number: S 11407_N23 name: Rigorous Systems Engineering - _id: 25F42A32-B435-11E9-9278-68D0E5697425 call_identifier: FWF grant_number: Z211 name: The Wittgenstein Prize publication_status: published publisher: Springer publist_id: '5818' quality_controlled: '1' related_material: record: - id: '1155' relation: dissertation_contains status: public scopus_import: 1 status: public title: Array folds logic type: conference user_id: 3E5EF7F0-F248-11E8-B48F-1D18A9856A87 volume: 9780 year: '2016' ...