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DOI: 10.4230/LIPIcs.ICALP.2018.114
URN: urn:nbn:de:0030-drops-91188
URL: https://drops.dagstuhl.de/opus/volltexte/2018/9118/
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 | |
| Seminar: | 45th International Colloquium on Automata, Languages, and Programming (ICALP 2018) | |
| Issue date: | 2018 | |
| Date of publication: | 04.07.2018 |
