Download On a Method of Multiprogramming (Monographs in Computer by W.H.J. Feijen, A.J.M. van Gasteren PDF

By W.H.J. Feijen, A.J.M. van Gasteren

The following, the authors suggest a mode for the formal improvement of parallel courses - or multiprograms as they like to name them. They accomplish this with not less than formal equipment, i.e. with the predicate calculus and the good- demonstrated idea of Owicki and Gries. They convey that the Owicki/Gries idea might be successfully positioned to paintings for the formal improvement of multiprograms, whether those algorithms are allotted or no longer.

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Thus the proof burden is reduecd from 2 x N to just 2 per invariant! We eonclude with thc observation that invariants Po and PI together imply thc invarianee of O:=:;x a result to be used below. End of Examplc 3. i: * [x:=x+1 ; {I:=:; x} x:=x-l 1 Inv: O:=:;x End of First Topology Lemma. Eaeh eomponent first inerements x and then deerements it. In between, thc value of x exceeds its initial value, irrespcetive of what the other eomponents have done to x. Sueh a eonfiguration pops up every so often, and having a theorcm about it has proven to be worthwhile.

As a result, the strongest R that we ean eonclude from the Core of Owieki and Gries is l:Sx 4. Two Disturbing Divergences 37 (which is definitely weaker than the intcnded x = 2 ). Acknowledgement We owe the abovc proof to our colleague Rob R. Hoogerwoord. End of Acknowledgcment. As will become apparent later, it is not the Core that is to bc blamed, but the fact that in the above example the value of x - which is the only variable in the game - cannot fully describe the states that thc system can reside in.

Q] for the loeal eorreetness of the two assertions P for the global eorreetness of the two assertions Q for the eorreetness of posteondition R. First observe that (3) is implied by (2), so that we ean forget about (3). Seeondly, observe from (4) that the strongest R equivales the strongest Q . And thus we are left with finding the strongest Q that is admitted by (0), (1), and (2). P - for a detailed proof see the Appendix of this ehapter. P with P satisfying (0) and (1) equivales 1:S x . As a result, the strongest R that we ean eonclude from the Core of Owieki and Gries is l:Sx 4.

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