Decision problems for linear recurrence sequences

Authors:
Joël Ouaknine;James Worrell
Affiliations:
Department of Computer Science, Oxford University, UK;Department of Computer Science, Oxford University, UK
Venue:
RP'12 Proceedings of the 6th international conference on Reachability Problems
Year:
2012

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Abstract

Linear recurrence sequences permeate a vast number of areas of mathematics and computer science. In this paper, we survey the state of the art concerning certain fundamental decision problems for linear recurrence sequences, namely the Skolem Problem (does the sequence have a zero?), the Positivity Problem (is the sequence always positive?), and the Ultimate Positivity Problem (is the sequence ultimately always positive?).