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The continuous Skolem-Pisot problem

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journal contribution
posted on 2013-04-04, 15:04 authored by Paul Bell, Jean-Charles Delvenne, Raphael M. Jungers, Vincent Blondel
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.

History

School

  • Science

Department

  • Computer Science

Citation

BELL, P.C. ... et al, 2010. The continuous Skolem-Pisot problem. Theoretical Computer Science, 411 (40-42), pp.3625-3634.

Publisher

© Elsevier

Version

  • AM (Accepted Manuscript)

Publication date

2010

Notes

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

ISSN

0304-3975

Language

  • en