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Decision Problems for Linear Recurrence Sequences

  • Joël Ouaknine
  • James Worrell
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7550)

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?).

Keywords

Decision Problem Recurrence Relation Algebraic Number Galois Theory Fibonacci Sequence 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Joël Ouaknine
    • 1
  • James Worrell
    • 1
  1. 1.Department of Computer ScienceOxford UniversityUK

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