The presence of a zero in an integer linear recurrent sequence is NP-hard to decide
(2002) Linear Algebra and Its Applications — Vol. 351, p. 91-98 (2002)
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- Abstract
- We show that the problem of determining if a given integer linear recurrent sequence has a zero-a problem that is known as "Pisot's problem"-is NP-hard. With a similar argument we show that the problem of finding the minimal realization dimension of a one-letter max-plus rational series is NP-hard. This last result answers a folklore question raised in the control literature on the max-plus approach to discrete event systems. Our results are simple consequences of a construction due to Stockmeyer and Meyer. (C) 2002 Elsevier Science Inc. All rights reserved.
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Blondel, V., & Portier, N. (2002). The presence of a zero in an integer linear recurrent sequence is NP-hard to decide. Linear Algebra and Its Applications, 351, 91-98. https://hdl.handle.net/2078.5/137885 (Original work published 2002)