The continuous Skolem-Pisot problem

Bell

doi:10.1016/j.tcs.2010.06.005

The continuous Skolem-Pisot problem

Bell

Authors

Paul Bell p.c.bell@keele.ac.uk

Abstract

We study decidability and complexity questions related to a continuous analogue of the Skolem-Pisot problem concerning the zeros and nonnegativity 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, including 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 differential equations, which are interesting problems in their own right.

Acceptance Date	Jun 6, 2010
Publication Date	Sep 6, 2010
Journal	Theoretical Computer Science
Print ISSN	0304-3975
Publisher	Elsevier
Pages	3625 - 3634
DOI	https://doi.org/10.1016/j.tcs.2010.06.005
Publisher URL	https://www.sciencedirect.com/science/article/pii/S0304397510003397?via%3Dihub