Download PDF by Howard Barringer: A Survey of Verification Techniques for Parallel Programs

By Howard Barringer

ISBN-10: 3540152393

ISBN-13: 9783540152392

ISBN-10: 3540394168

ISBN-13: 9783540394167

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Q~Dn {I(M) . . . . SEND I I COMP l ^ . . COMP2 II II ... COMPN II . . SEND : : . . . . . . . . . . . . . . . . . ___dd { NPo = j } end { . . . . SORT} . . . . } NPo=N . . . . . . . . . . . . . . . . . the number of ) version in 49 COMP~ :: ~$~h M ( $ ) =hen ~ r d ~ ( $ ) { I(M) ^ ~ r d p ( ~ ) do ^ NP~ = 0 } beg~n NP$ := I end; {Np~ for j = I } ~= I un~ N - ~ do ~fne_Dn ( ~ r d ~ ( ~ ) ^ rdy(~+1)) do beaSn s~ := max(A(~),S~); rdy(~) := #rue; rdy(~+l) NP~ := f o L s e ; := NP~.

Sequential" proofs are obtained as above and the precondition (postcondition) for the parallel execution of the processes is taken as conjunction of the preconditions (postconditions) from the isolated proofs, together with the resource invariant. 6 provides a short summary inference rules for the parallelism parts from the axiomatisations of both RPL and GPL. 3 ORIGINAL EXAMPLES The paper [OG76a], which presents the more considers two main exanE01es, cot%0onent of an array which is problem. whereas Both the the Findpos greater than primitive parallel language GPL, program of Rosen ( finding the first zero and ) the producer consumer partial correctness and termination proofs are given for the former, latter, implementations, which has appears partial in two correctness [OG76b], presenting the 'not so primitive' differing semaphore and deadlock freedom proofs.

P } u~,~h r u h e n R3. ~hen statements of process S k ~ . : - skJ -~ u¢~h rkJ ~hen BkJ ~ TkJ, I~J~nk L e t p r e ( S k J ) and I(r) b e assertions derived from a p r o o f o f {P} S {Q}. L e t D1 ~ A k (pos~(S~) D2 ~ V k V~ (-~kJ ^ pre(Sk,])) Then if DI ^ £)2 ^ I(r) W exec~t ion begins. , Francez, N. P. A proof system for communicating sequential processes. ~CM TOPLAS, Vol. 2, NO. 3, July 1980, pp. 359-385. R. Formal justification of a proof system for cormnunicating sequential processes, JACM, Vol.

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A Survey of Verification Techniques for Parallel Programs by Howard Barringer


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