The continuous Skolem-Pisot problem

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.