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The presence of a zero in an integer linear recurrent sequence is NP-hard to decide

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Blondel, Vincent [UCL] Portier, N

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.

Document type Article de périodique (Journal article) – Article de recherche
Publication date 2002
Language Anglais
Journal information "Linear Algebra and Its Applications" - Vol. 351, p. 91-98 (2002)
Peer reviewed yes
Publisher Elsevier Science Inc (New York)
issn 0024-3795
e-issn 1873-1856
Publication status Publié
Affiliation UCL
Keywords Pisot's problem ; linear recurrent sequence ; minimal realization ; max-plus rational series
Links
Bibliographic reference Blondel, Vincent ; Portier, N. The presence of a zero in an integer linear recurrent sequence is NP-hard to decide. In: Linear Algebra and Its Applications, Vol. 351, p. 91-98 (2002)
Permanent URL http://hdl.handle.net/2078.1/41798