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Degree and Dimension Estimates for Invariant Ideals of $$P$$ -Solvable Recurrences

In: Computer Mathematics

Author

Listed:
  • Marc Moreno Maza

    (University of Western Ontario)

  • Rong Xiao

    (University of Western Ontario)

Abstract

Motivated by the generation of polynomial loop invariants of computer programs, we study $$P$$ -solvable recurrences. While these recurrences may contain non-linear terms, we show that the solutions of any such relation can be obtained by solving a system of linear recurrences. We also study invariant ideals of $$P$$ -solvable recurrences (or equivalently of while loops with no branches). We establish sharp degree and dimension estimates of those invariant ideals.

Suggested Citation

  • Marc Moreno Maza & Rong Xiao, 2014. "Degree and Dimension Estimates for Invariant Ideals of $$P$$ -Solvable Recurrences," Springer Books, in: Ruyong Feng & Wen-shin Lee & Yosuke Sato (ed.), Computer Mathematics, edition 127, pages 349-373, Springer.
    • Handle: RePEc:spr:sprchp:978-3-662-43799-5_25
    DOI: 10.1007/978-3-662-43799-5_25
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