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URN: urn:nbn:de:0030-drops-144953
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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


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