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On Extending Bounded Proofs to Inductive Proofs

  • Oded Fuhrmann
  • Shlomo Hoory
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5643)

Abstract

We propose a method for extending a bounded resolution proof to an unbounded inductive proof. More specifically, given a resolution proof that a state machine beginning at an initial state satisfies some property at cycle k, we show that the existence of a Δ-invariant cut implies that the property holds for cycles k + Δ, k + 2Δ, etc. We suggest a linear algorithm for identifying such Δ-extendible proofs and develop the required theory for covering all cycles by Δ-extendible proofs. To expose Δ-invariant cuts, we develop an efficient proof manipulation algorithm that rearranges the proof by the natural temporal order. We demonstrate the applicability of our techniques on a few real-life examples.

Keywords

Formal verification resolution proofs extending proofs proof simplification 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2009

Authors and Affiliations

  • Oded Fuhrmann
    • 1
  • Shlomo Hoory
    • 1
  1. 1.IBM Haifa Research LabIsrael

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