Degree and Dimension Estimates for Invariant Ideals of \(P\)-Solvable Recurrences

  • Marc Moreno MazaEmail author
  • Rong XiaoEmail author
Conference paper


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.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2014

Authors and Affiliations

  1. 1.University of Western OntarioLondonCanada

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