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Mechanizing a Correctness Proof for a Lock-Free Concurrent Stack

  • John Derrick
  • Gerhard Schellhorn
  • Heike Wehrheim
Part of the Lecture Notes in Computer Science book series (LNCS, volume 5051)

Abstract

Distributed algorithms are inherently complex to verify. In this paper we show how to verify that a concurrent lock-free implementation of a stack is correct by mechanizing the proof that it is linearizable, linearizability being a correctness notion for concurrent objects. Our approach consists of two parts: the first part is independent of the example and derives proof obligations local for one process which imply linearizabilty. The conditions establish a (special sort of non-atomic) refinement relationship between the specification and the concurrent implementation. These are used in the second part to verify the lock-free stack implementation. We use the specification language Z to describe the algorithms and the KIV theorem prover to mechanize the proof.

Keywords

refinement concurrent access linearizability non-atomic refinement theorem proving KIV 

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Copyright information

© Springer-Verlag Berlin Heidelberg 2008

Authors and Affiliations

  • John Derrick
    • 1
  • Gerhard Schellhorn
    • 2
  • Heike Wehrheim
    • 3
  1. 1.Department of ComputingUniversity of SheffieldSheffieldUK
  2. 2.Institut für InformatikUniversität AugsburgAugsburgGermany
  3. 3.Institut für InformatikUniversität PaderbornPaderbornGermany

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