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A theorem on atomicity in distributed algorithms

Abstract

Reasoning about a distributed algorithm is simplified if we can ignore the time needed to send and deliver messages and can instead pretend that a process sends a collection of messages as a single atomic action, with the messages delivered instantaneously as part of the action. A theorem is derived that proves the validity of such reasoning for a large class of algorithms. It generalizes and corrects a well-known folk theorem about when an operation in a multiprocess program can be considered atomic.

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Abbreviations

A :

The set of program actions

A :

The algorithm under consideration

A :

The reduced version of algorithmA

A〉:

The action obtained by executing the operationA as an atomic action

C :

The set of state components

d[i]:

A variable of the Distance-Finding Algorithm

L :

An operation ofA, as in C2

Ľ :

The operation obtained by adding toL the actions that deliver messages sent byL

N p(S):

The set of possible next actions of processp from states

P :

The correctness property

R :

An operation ofA, as in C2

S :

The set of states

S 0 :

The set of initial states

S c :

The range of values of state componentc

X〉:

An action ofA, as in C2

Φ:

Usually denotes an execution ofA

∑:

The execution ofA that corresponds to an execution Φ ofA

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Additional information

When snow conditions are poor,Dr. L. Lamport works at Digital Equipment Corporation's Systems Research Center. As an undergraduate, he took a course in atomic physics.

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Lamport, L. A theorem on atomicity in distributed algorithms. Distrib Comput 4, 59–68 (1990). https://doi.org/10.1007/BF01786631

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Key words

  • Message passing
  • Reduction