A Formal Proof of a Necessary and Sufficient Condition for Deadlock-Free Adaptive Networks

  • Freek Verbeek
  • Julien Schmaltz
Conference paper

DOI: 10.1007/978-3-642-14052-5_7

Part of the Lecture Notes in Computer Science book series (LNCS, volume 6172)
Cite this paper as:
Verbeek F., Schmaltz J. (2010) A Formal Proof of a Necessary and Sufficient Condition for Deadlock-Free Adaptive Networks. In: Kaufmann M., Paulson L.C. (eds) Interactive Theorem Proving. ITP 2010. Lecture Notes in Computer Science, vol 6172. Springer, Berlin, Heidelberg

Abstract

Deadlocks occur in interconnection networks as messages compete for free channels or empty buffers. Deadlocks are often associated with a circular wait between processes and resources. In the context of networks, Duato proved that for adaptive routing networks a cyclic dependency is not sufficient to create a deadlock. He proposed deadlock-free routing techniques allowing cyclic dependencies between channels or buffers. His work was a breakthrough. It was also counterintuitive and only a complex mathematical proof could convince his peers about the soundness of his theory. We define a necessary and sufficient condition that captures Duato’s intuition but that is more intuitive and leads to a simpler proof. However, our condition is logically equivalent to Duato’s one. We used the ACL2 theorem proving system to formalize our condition and its proof. In particular, we used two features of ACL2, namely the encapsulation principle and quantifiers, to perform an elegant formalization based on second order functions.

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Copyright information

© Springer-Verlag Berlin Heidelberg 2010

Authors and Affiliations

  • Freek Verbeek
    • 1
    • 2
  • Julien Schmaltz
    • 1
    • 2
  1. 1.Institute for Computing and Information SciencesRadboud University NijmegenNijmegenThe Netherlands
  2. 2.School of Computer ScienceOpen University of the NetherlandsHeerlenThe Netherlands

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