David Gries

An axiomatic proof technique for parallel programs I

SummaryA language for parallel programming, with a primitive construct for synchronization and mutual exclusion, is presented. Hoares deductive system for proving partial correctness of sequential programs is extended to include the parallelism described by the language. The proof method lends insight into how one should understand and present parallel programs. Examples are given using several of the standard problems in the literature. Methods for proving termination and the absence of deadlock are also given.

Finding Repeated Elements

Two algorithms are presented for finding the values that occur more than

Translator writing systems

n \div k

The Programming Language Ada Reference Manual

times in array b[O:n-1]. The second algorithm requires time

A proof technique for communicating sequential processes

O(n \log(k))

A constructive proof of Vizing's Theorem

and extra space

An exercise in proving parallel programs correct

O(k)

Describing an algorithm by Hopcroft

. We prove that

Fault-tolerant broadcasts

O(n \log(k))

Assignment and Procedure Call Proof Rules

is a lower bound on the time required for any algorithm based on comparing array elements, so that the second algorithm is optimal. As special cases, determining whether a value occurs more than