By Howard Barringer
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Additional info for A Survey of Verification Techniques for Parallel Programs
The processes SmaLL variables ~ and Lo~rge c o m m u n i c a t e w i t h e a c h o t h e r b y use o f the and ran. T h e shared v a r i a b l e s r m x and Finn s y n c h r o n i z e the r e a d i n g and w r i t i n g o f the s h a r e d variables; w h e n rtr~ ( F i n n ) is Erue, it indicates that m~ ( ran) is by using a r e a d y to b e read. N o t e t h a t w e c o u l d h a v e w r i t t e n the repeo$ .. un¢$L loop form. program p r o o f s o f the i s o l a t e d processes.
In David Gries's collector is paper presented. [Gr77], This a larger proof of example Dijkstra's clearly on-the-fly shows the garbage difficulty in demonstrating interfering programs correct. 4. 1 EXAMPLE i. P~/~TITIONING of SETS We give a solution to the partition problem (after Dijkstra). two non-empty disjoint sets of integers. The problem is to partition them so that the nkxximtna element of one is less than the minimum element of the condition that the sets Initially we have stay the same size.
Dd . . . . . . . . . . . . . . . . . . . . . . . . . . . . . COMP S :: do beGSn rd11(S) := t r u e end; ~or J := I un~S& N-S ~o___beaSn uS#h M(S), M(S+I) u h e n ~ r d y ( S ) A(S+I) ^ rd~(S+1) := m S n ( A ( ~ ) , B s ) ; ss = = m a z ( a ( S ) , s S ) ; rdy(S) := srue; r~l;(~+1) : = fa~es en~ en___dd . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 Partial Correctness qf BL S O R T We require as precondition and postcondition:pre-BL_SORT e ~en(&n) = ~en(A) = Den(S) = N ^N~O ^ NP0 = 0 ^ Yl, ~ I .