License: Creative Commons Attribution 3.0 Unported license (CC BY 3.0)
When quoting this document, please refer to the following
DOI: 10.4230/LIPIcs.ICALP.2018.114
URN: urn:nbn:de:0030-drops-91188
URL: http://dagstuhl.sunsite.rwth-aachen.de/volltexte/2018/9118/
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Almagor, Shaull ; Chistikov, Dmitry ; Ouaknine, Joël ; Worrell, James

O-Minimal Invariants for Linear Loops

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Abstract

The termination analysis of linear loops plays a key rôle in several areas of computer science, including program verification and abstract interpretation. Such deceptively simple questions also relate to a number of deep open problems, such as the decidability of the Skolem and Positivity Problems for linear recurrence sequences, or equivalently reachability questions for discrete-time linear dynamical systems. In this paper, we introduce the class of o-minimal invariants, which is broader than any previously considered, and study the decidability of the existence and algorithmic synthesis of such invariants as certificates of non-termination for linear loops equipped with a large class of halting conditions. We establish two main decidability results, one of them conditional on Schanuel's conjecture in transcendental number theory.

BibTeX - Entry

@InProceedings{almagor_et_al:LIPIcs:2018:9118,
  author =	{Shaull Almagor and Dmitry Chistikov and Jo{\"e}l Ouaknine and James Worrell},
  title =	{{O-Minimal Invariants for Linear Loops}},
  booktitle =	{45th International Colloquium on Automata, Languages, and  Programming (ICALP 2018)},
  pages =	{114:1--114:14},
  series =	{Leibniz International Proceedings in Informatics (LIPIcs)},
  ISBN =	{978-3-95977-076-7},
  ISSN =	{1868-8969},
  year =	{2018},
  volume =	{107},
  editor =	{Ioannis Chatzigiannakis and Christos Kaklamanis and D{\'a}niel Marx and Donald Sannella},
  publisher =	{Schloss Dagstuhl--Leibniz-Zentrum fuer Informatik},
  address =	{Dagstuhl, Germany},
  URL =		{http://drops.dagstuhl.de/opus/volltexte/2018/9118},
  URN =		{urn:nbn:de:0030-drops-91188},
  doi =		{10.4230/LIPIcs.ICALP.2018.114},
  annote =	{Keywords: Invariants, linear loops, linear dynamical systems, non-termination, o-minimality}
}

Keywords: Invariants, linear loops, linear dynamical systems, non-termination, o-minimality
Collection: 45th International Colloquium on Automata, Languages, and Programming (ICALP 2018)
Issue Date: 2018
Date of publication: 04.07.2018

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