Development of a concurrent program in Software Use Data Matrix in Software Development of a concurrent program

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Development of a concurrent program using barcode integrated for software control to generate, create datamatrix image in software applications. About QR Code below: inv1_3: u Software datamatrix 2d barcode = g(r) variables: ...

u m y inv1_4: m = f (r) inv1_5: y D inv1_6: adr_r = 1 y = rd(r). 7.6.2 The reading events The reader events are now de ned below.

We have two new events (re ning skip): Reader_1 and Reader_3. For the moment, event Reader_1 is just a dummy. Abstract event read is renamed Reader_2.

This is illustrated in Fig. 7.10.

. skip refines read refines skip refines Reader_1. (dummy). Reader_ Reader_2. Reader_3. Fig. 7.10. Re nement of the reader Among the three e vents, Reader_2 is the one that re nes the abstract event read. The reason for this choice is explained informally by looking at the Reader program: Reader reading := latest; indx_r := slot(reading); y := data(reading)(indx_r) In fact, it happens that after the second instruction of this program, the data which are read, namely data(reading)(indx_r), do not change whatever the behavior of the writing programs. This will be proved formally in the fourth re nement.

So we choose. 7.6 First re nement to state that wha t is read is de ned after the second instruction, hence our choice of re ning event read with event Reader_2. In event Reader_2, the non-deterministic choice for v, which was in g(r) ..

w in the abstraction, is now in u .. w (remember invariant inv1_3, which says that u is equal to g(r)).

The result of the reading in variable y is done in event Reader_3. Remember that invariant inv1_6 says that just after an occurrence of event Reader_3 (when adr_r is equal to 1), y is equal to the last item of the reading trace, rd(r), which is wtp(f (r)) that is wtp(m) since m = f (r) (this is invariant inv1_4): Reader_2 re nes read any v where adr_r = 2 v u ..

w then m := v u := w adr_r := 3 end. Reader_1 when adr_r = 1 then adr_r := 2 end Reader_3 when adr_r = 3 then y := wtp(m) adr_r := 1 end 7.6.3 The writer Software data matrix barcodes state We de ne now the concrete writing trace wtp, which is slightly di erent from the abstract writing trace wt.

It is di erent because, in this re nement, the writing trace wtp is modi ed in an event (Writer_1), while the writing index w is incremented in two different events: Writer_42 or Writer_51. All this is expressed in the following invariants: wtp N1 D wt wtp adr_w = 1 dom(wtp) = 1 ..

w. inv1_7: inv1_8: v ariables: ...

wtp inv1_9:. inv1_10: adr_w datamatrix 2d barcode for None {2, 3, 4} dom(wtp) = 1 .. w + 1 inv1_11: adr_w = 5 dom(wtp) {1 .

. w, 1 ..

w + 1}. Development of a concurrent program 7.6.4 The writing Data Matrix barcode for None events Now come the writing events.

We have ve new events (re ning skip): Writer_1, Writer_2, Writer_3, Writer_41, and Writer_52. For the moment, events Writer_2, Writer_3, Writer_41, and Writer_52 are simple dummies. Events Writer_42 and Writer_51 are both re ning abstract event write.

All this is illustrated in Fig. 7.11.

. skip refines refines skip refines skip refines skip refines write refines refines skip Writer_1. Writer_2. (dummy). Writer_3. (dummy). Writer_41. (dummy). Writer_42. Writer_51. Writer_52. (dummy). Fig. 7.11. Re nement of the writer The choice of the Software Data Matrix barcode event re ning abstract event write is more delicate than that for the reading case. To explain it informally, let us study the Writer program:. Writer(x) pair_w := 1 reading; indx_w := 1 slot(pair_w); data(pair_w)(indx_w) := x slot(pair_w) := indx_w; latest := pair_w. The instruction t Software Data Matrix barcode hat must correspond to what we can observe in the abstraction is not the third one where the writing is done. The reason for not choosing that instruction is that the last two instructions modify some data (slot and latest) which are shared. 7.6 First re nement by the Reader pro Software datamatrix 2d barcode gram. So, we have to choose the last instruction. But, in fact, this last instruction is sometimes doing nothing; this is when latest is already equal to pair_w.

It can happen when the Reader program has been quiet for a while and has not modi ed the variable reading. In that case, pair_w is not modi ed in the rst instruction; hence latest is not modi ed. As a consequence, the abstract end of the writing is either on the fourth or on the fth instruction.

Therefore, we de ne two events for the fourth instruction, Writer_41 and Writer_42, and two events for the fth instruction, Writer_51 and Writer_52. The writing in wtp occurs in event Writer_1, while the incrementation of the index w is only done in event Writer_42 or Writer_51. Note the guards in events Writer_51 and Writer_52.

They ensure that w is always incremented, but only once either in event Writer_42 or in event Writer_51:.
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