By W.H.J. Feijen
Right here, the authors suggest a style for the formal improvement of parallel courses - or multiprograms as they like to name them. They accomplish this with at the least formal apparatus, i.e. with the predicate calculus and the good- confirmed concept of Owicki and Gries. They convey that the Owicki/Gries idea will be successfully placed to paintings for the formal improvement of multiprograms, whether those algorithms are allotted or no longer.
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Extra info for On a Method of Multiprogramming (Monographs in Computer Science)
If the method with no part X has procedure invariant P, then P is an accurate pre-assertion of X. end up this. (This is a very easy "composition" theorem, which could occasionally be used at nice virtue. The reader may perhaps now desire to revisit the former workout. ) workout 17 think about the next two-component multiprogram: x=X 1\ y=Y B: A: ! :=y g:=x ; y:=g ; x:=! Pre: Synchronize, utilizing one-point-statements simply, the parts such that the postcondition will indicate a. x=Y b. x= Y 1\ y=X c. x=X 1\ y=X d. x=y 138 12. The phone book workout 18 if B convey that atomic assertion eight fi ---+ of a few part might be changed with the finer grained if B bypass fi ---+ ;8 with out affecting correctness, supplied B is globally right. (Rint: use the protect Conjunction Lemma. ) (In operational phrases, this theorem tells us that execution of S should be postponed, each time B can't be falsified through the remainder of the approach. ) workout 19 ponder the subsequent multiprogram: n=O /\ s=O Pre: A: * [n:=n+l ; s:=s+1 1 B: * [ if 1 ~ s ---+ s := s - 1 fi ; n:=n-l 1 C: * [ if 1 ~ s ---+ s := s -1 fi ; n:=n-l 1 (Note that the operations on eight mimic P- and V- operations. ) convey the invariance of zero ~ n. What if the guarded skips in Band C are changed by way of the finer grained if 1 ~ s ---+ pass fi ; s :=s-1 ? subsequent, we cut up "semaphore" s within the above set of rules into "semaphores" sb and sc through the co ordinate transformation o~ sb /\ zero ~ sc /\ s = sb + sc We could hence receive 12. 1 workouts Prc: A: 139 n = zero 1\ sb = zero 1\ sc = zero * [n:=n+l ; if ( actual ) ~ ( sb := sb + 1 ) ~ ( precise ) ~ ( sc := sc + 1 ) fi J B: * [ if 1 '5. sb ~ sb := sb - 1 fi ; n:=n-l 1 C: * [ if 1 '5. sc ~ sc : = sc - 1 fi ; n:=n-l J (The angular brackets in A point out the meant granularity of that if-statement. ) Argue why 0'5. n nonetheless is a process invariant. express that the guarded assertion in B could be changed with the finer grained if 1 '5. sb ~ bypass fi ; sb := sb-l Likewise for C. workout 20 Pre: contemplate two-component multiprogram x = zero 1\ Y = zero A: *[x:=x+l] I B: *[y:=y+l] Synchronize the elements ~ utilizing guarded skips in basic terms ~ such that x '5. y should be a process invariant. the best way to do that if x or y should not allowed to ensue within the synchronization protocol? What if there are a number of parts of kind A and a number of other of sort B? workout 21 give some thought to the subsequent multiprogram, with 23 parts of variety A and forty seven elements of variety B: 140 12. The phone book Pre: eight =0 B: * [ 8:= eight -1 J A: *[8:=8+1J Synchronize the elements --- utilizing guarded skips purely -- such that o~ eight ~ a hundred could be a approach invariant. workout 22 Pre: convey the invariance of lnv in x=O A y=O A z=O A: *[x:=x+1; y:= y-1] B: * [y:=y+1; z := z-l J C: * [z:=z+l; x := x-I J lnv: 0~x+y+z~3 subsequent, synchronize the parts such that they're going to continue O~x A x~y A y~z speak about person development. workout 23 Pre: give some thought to the subsequent many-component multiprogram: ( Vq :: -'X. q ) Comp.