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A LatticeStructured Proof Technique Applied to a Minimum Spanning Tree Algorithm (Extended Abstract)
 Laboratory for Computer Science, Massachusetts Institute of Technology
, 1988
"... Jennifer Lundelius Welch Leslie Lamport Digital Equipment Corporation, Systems Research Center Abstract: rithms are often hard to prove correct because they have no natural decomposition into separately provable parts. This paper presents a proof technique for the modular verification of su ..."
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Cited by 12 (3 self)
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Jennifer Lundelius Welch Leslie Lamport Digital Equipment Corporation, Systems Research Center Abstract: rithms are often hard to prove correct because they have no natural decomposition into separately provable parts. This paper presents a proof technique for the modular verification of such nonmodular algorithms. It generalizes existing verification techniques based on a totallyordered hierarchy of refinements to allow a partiallyordered hierarchythat is; a lattice of different views of the algorithm. The technique is applied to the wellknown distributed minimum spanning tree algorithm of Gallager, Humblet and Spira, which has until recently lacked a rigorous proof. 1.
A Modular Drinking Philosophers Algorithm
 Distributed Computing
, 2001
"... A variant of the drinking philosophers algorithm of Chandy and Misra is described and proved correct in a modular way. The algorithm of Chandy and Misra is based on a particular dining philosophers algorithm and relies on certain properties of its implementation. The drinking philosophers algorit ..."
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Cited by 8 (0 self)
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A variant of the drinking philosophers algorithm of Chandy and Misra is described and proved correct in a modular way. The algorithm of Chandy and Misra is based on a particular dining philosophers algorithm and relies on certain properties of its implementation. The drinking philosophers algorithm presented in this paper is able to use an arbitrary dining philosophers algorithm as a subroutine; nothing about the implementation needs to be known, only that it solves the dining philosophers problem. An important advantage of this modularity is that by substituting a more timeefficient dining philosophers algorithm than the one used by Chandy and Misra, a drinking philosophers algorithm with O(1) worstcase waiting time is obtained, whereas the drinking philosophers algorithm of Chandy and Misra has O(n) worstcase waiting time (for n philosophers). Careful definitions are given to distinguish the drinking and dining philosophers problems and to specify varying degrees of concurrency.