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On Ranking Function Synthesis and Termination for Polynomial Programs

Authors Eike Neumann, Joël Ouaknine, James Worrell



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Author Details

Eike Neumann
  • Department of Computer Science, Oxford University, UK
Joël Ouaknine
  • Max Planck Institute for Software Systems, Saarland Informatics Campus, Saarbrücken, Germany
  • Department of Computer Science, Oxford University, UK
James Worrell
  • Department of Computer Science, Oxford University, UK

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Eike Neumann, Joël Ouaknine, and James Worrell. On Ranking Function Synthesis and Termination for Polynomial Programs. In 31st International Conference on Concurrency Theory (CONCUR 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 171, pp. 15:1-15:15, Schloss Dagstuhl - Leibniz-Zentrum für Informatik (2020)
https://doi.org/10.4230/LIPIcs.CONCUR.2020.15

Abstract

We consider the problem of synthesising polynomial ranking functions for single-path loops over the reals with continuous semi-algebraic update function and compact semi-algebraic guard set. We show that a loop of this form has a polynomial ranking function if and only if it terminates. We further show that termination is decidable for such loops in the special case where the update function is affine.

Subject Classification

ACM Subject Classification
  • Theory of computation → Semantics and reasoning
Keywords
  • Semi-algebraic sets
  • Polynomial ranking functions
  • Polynomial programs

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References

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