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Title: The continuous Skolem-Pisot problem
Authors: Bell, Paul C.
Delvenne, Jean-Charles
Jungers, Raphael M.
Blondel, Vincent
Keywords: Skolem-Pisot problem
Exponential polynomials
Continuous time dynamical system
Ordinary differential equations
Issue Date: 2010
Publisher: © Elsevier
Citation: BELL, P.C. ... et al, 2010. The continuous Skolem-Pisot problem. Theoretical Computer Science, 411 (40-42), pp.3625-3634.
Abstract: We study decidability and complexity questions related to a continu- ous analogue of the Skolem-Pisot problem concerning the zeros and non- negativity of a linear recurrent sequence. In particular, we show that the continuous version of the nonnegativity problem is NP-hard in general and we show that the presence of a zero is decidable for several subcases, in- cluding instances of depth two or less, although the decidability in general is left open. The problems may also be stated as reachability problems related to real zeros of exponential polynomials or solutions to initial value problems of linear dfferential equations, which are interesting problems in their own right.
Description: This is the author’s version of a work that was accepted for publication in the journal Theoretical Computer Science. Changes resulting from the publishing process, such as peer review, editing, corrections, structural formatting, and other quality control mechanisms may not be reflected in this document. Changes may have been made to this work since it was submitted for publication. A definitive version was subsequently published at: http://dx.doi.org/10.1016/j.tcs.2010.06.005
Version: Accepted for publication
DOI: 10.1016/j.tcs.2010.06.005
URI: https://dspace.lboro.ac.uk/2134/12043
Publisher Link: http://dx.doi.org/10.1016/j.tcs.2010.06.005
ISSN: 0304-3975
Appears in Collections:Published Articles (Computer Science)

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