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

AbstractWe 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