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DOI: 10.4230/LIPIcs.MFCS.2021.55
URN: urn:nbn:de:0030-drops-144953
URL: https://drops.dagstuhl.de/opus/volltexte/2021/14495/
Haase, Christoph ; Mansutti, Alessio
On Deciding Linear Arithmetic Constraints Over p-adic Integers for All Primes
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Abstract
Given an existential formula Φ of linear arithmetic over p-adic integers together with valuation constraints, we study the p-universality problem which consists of deciding whether Φ is satisfiable for all primes p, and the analogous problem for the closely related existential theory of Büchi arithmetic. Our main result is a coNEXP upper bound for both problems, together with a matching lower bound for existential Büchi arithmetic. On a technical level, our results are obtained from analysing properties of a certain class of p-automata, finite-state automata whose languages encode sets of tuples of natural numbers.
BibTeX - Entry
@InProceedings{haase_et_al:LIPIcs.MFCS.2021.55,
author = {Haase, Christoph and Mansutti, Alessio},
title = {{On Deciding Linear Arithmetic Constraints Over p-adic Integers for All Primes}},
booktitle = {46th International Symposium on Mathematical Foundations of Computer Science (MFCS 2021)},
pages = {55:1--55:20},
series = {Leibniz International Proceedings in Informatics (LIPIcs)},
ISBN = {978-3-95977-201-3},
ISSN = {1868-8969},
year = {2021},
volume = {202},
editor = {Bonchi, Filippo and Puglisi, Simon J.},
publisher = {Schloss Dagstuhl -- Leibniz-Zentrum f{\"u}r Informatik},
address = {Dagstuhl, Germany},
URL = {https://drops.dagstuhl.de/opus/volltexte/2021/14495},
URN = {urn:nbn:de:0030-drops-144953},
doi = {10.4230/LIPIcs.MFCS.2021.55},
annote = {Keywords: linear arithmetic, B\"{u}chi arithmetic, p-adic numbers, automatic structures}
}
| Keywords: | linear arithmetic, Büchi arithmetic, p-adic numbers, automatic structures | |
| Seminar: | 46th International Symposium on Mathematical Foundations of Computer Science (MFCS 2021) | |
| Issue date: | 2021 | |
| Date of publication: | 18.08.2021 |
