Synthesis of Linear Ranking Functions

  • Michael A. Colóon
  • Henny B. Sipma
Conference paper

DOI: 10.1007/3-540-45319-9_6

Volume 2031 of the book series Lecture Notes in Computer Science (LNCS)
Cite this paper as:
Colóon M.A., Sipma H.B. (2001) Synthesis of Linear Ranking Functions. In: Margaria T., Yi W. (eds) Tools and Algorithms for the Construction and Analysis of Systems. TACAS 2001. Lecture Notes in Computer Science, vol 2031. Springer, Berlin, Heidelberg

Abstract

Deductive verification of progress properties relies on finding ranking functions to prove termination of program cycles. We present an algorithm to synthesize linear ranking functions that can establish such termination. Fundamental to our approach is the representation of systems of linear inequalities and sets of linear expressions as polyhedral cones. This representation allows us to reduce the search for linear ranking functions to the computation of polars, intersections and projections of polyhedral cones, problems which have well-known solutions.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2001

Authors and Affiliations

  • Michael A. Colóon
    • 1
  • Henny B. Sipma
    • 1
  1. 1.Computer Science DepartmentStanford UniversityStanford