The Continuous Skolem-Pisot Problem: On the Complexity of Reachability for Linear Ordinary Differential Equations

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dc.creatorBell, Paul
dc.creatorDelvenne, Jean-Charles
dc.creatorJungers, Raphael
dc.creatorBlondel, Vincent D.
dc.date2008-09-12
dc.date2009-04-23
dc.date.accessioned2026-07-07T13:07:04Z
dc.date.available2026-07-07T13:07:04Z
dc.descriptionWe 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.
dc.description14 pages, no figure
dc.identifierhttps://arxiv.org/abs/0809.2189
dc.identifierhttp://arxiv.org/abs/0809.2189
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/227977
dc.subjectDynamical Systems
dc.subject37C99
dc.titleThe Continuous Skolem-Pisot Problem: On the Complexity of Reachability for Linear Ordinary Differential Equations
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