Abstract Partial Cylindrical Algebraic Decomposition I: The Lifting Phase

  • Grant Olney Passmore
  • Paul B. Jackson
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7318)

Abstract

Though decidable, the theory of real closed fields (RCF) is fundamentally infeasible. This is unfortunate, as automatic proof methods for nonlinear real arithmetic are crucially needed in both formalised mathematics and the verification of real-world cyber-physical systems. Consequently, many researchers have proposed fast, sound but incomplete RCF proof procedures which are useful in various practical applications. We show how such practically useful, sound but incomplete RCF proof methods may be systematically utilised in the context of a complete RCF proof method without sacrificing its completeness. In particular, we present an extension of the RCF quantifier elimination method Partial CAD (P-CAD) which uses incomplete ∃ RCF proof procedures to “short-circuit” expensive computations during the lifting phase of P-CAD. We present the theoretical framework and preliminary experiments arising from an implementation in our RCF proof tool RAHD.

Keywords

Sample Point Satisfying Assignment Expensive Computation Proof Procedure Real Closed Field 
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

  • Grant Olney Passmore
    • 1
    • 2
  • Paul B. Jackson
    • 2
  1. 1.Clare Hall, University of CambridgeCambridgeUnited Kingdom
  2. 2.Laboratory for Foundations of Computer Science, School of InformaticsUniversity of EdinburghEdinburghScotland

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