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DOI: 10.4230/LIPIcs.TIME.2020.17
URN: urn:nbn:de:0030-drops-129850
URL: https://drops.dagstuhl.de/opus/volltexte/2020/12985/
Bednarczyk, Bartosz ; Witkowski, Piotr
A Note on C² Interpreted over Finite Data-Words
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Abstract
We consider the satisfiability problem for the two-variable fragment of first-order logic extended with counting quantifiers, interpreted over finite words with data, denoted here with C²[≤ , succ, ∼, π_bin]. In our scenario, we allow for using arbitrary many uninterpreted binary predicates from π_bin, two navigational predicates ≤ and succ over word positions as well as a data-equality predicate ∼. We prove that the obtained logic is undecidable, which contrasts with the decidability of the logic without counting by Montanari, Pazzaglia and Sala [Angelo Montanari et al., 2016]. We supplement our results with decidability for several sub-fragments of C²[≤ , succ, ∼, π_bin], e.g. without binary predicates, without successor succ, or under the assumption that the total number of positions carrying the same data value in a data-word is bounded by an a priori given constant.
BibTeX - Entry
@InProceedings{bednarczyk_et_al:LIPIcs:2020:12985,
author = {Bartosz Bednarczyk and Piotr Witkowski},
title = {{A Note on C² Interpreted over Finite Data-Words}},
booktitle = {27th International Symposium on Temporal Representation and Reasoning (TIME 2020)},
pages = {17:1--17:14},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-167-2},
ISSN = {1868-8969},
year = {2020},
volume = {178},
editor = {Emilio Mu{\~n}oz-Velasco and Ana Ozaki and Martin Theobald},
publisher = {Schloss Dagstuhl--Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/opus/volltexte/2020/12985},
URN = {urn:nbn:de:0030-drops-129850},
doi = {10.4230/LIPIcs.TIME.2020.17},
annote = {Keywords: Two-variable logic, data-words, VASS, decidability, undecidability, counting}
}
| Keywords: | Two-variable logic, data-words, VASS, decidability, undecidability, counting | |
| Seminar: | 27th International Symposium on Temporal Representation and Reasoning (TIME 2020) | |
| Issue date: | 2020 | |
| Date of publication: | 15.09.2020 |
