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Visual Studio .NET barcode cir0 when mode = cir r1 = a1 r2 = a2 then mode := env p1 := FALSE p2 := FALSE end in Software Make Data Matrix ECC200 in Software cir0 when mode = cir r1 = a1 r2 = a2 then mode := env p1 := FALSE p2 := FALSE end




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cir0 when mode = cir r1 = a1 r2 = a2 then mode := env p1 := FALSE p2 := FALSE end using none touse none in asp.net web,windows applicationqr barcode generator c# + free Proving deadlock fre none none edom Nothing guarantees, of course, that the circuit events are not stuck because their guards do not hold. We have thus to prove the following, stating that while in the cir mode, the disjunction of the guards of the circuit always. Java Platform 8.3 Second example: the arbiter holds: r1 = a1 p2 = FALSE mode = cir r2 = a2 p1 = FALSE r1 = a1 r2 = a2 thm0_1:. To prove this, it is none none necessary to add the following invariants:. inv0_14: mode = cir (r1 = a1 p1 = FALSE) inv0_15: mode = cir (r2 = a2 p2 = FALSE). Note that the circui none for none t is still non-deterministic; this is the case when both users are just require the resource simultaneously (thus p1 = FALSE and p2 = FALSE hold simultaneously). In this case, both circuit events, cir1 and cir2, can be red..

8.3.3 First re nemen t: generating binary outputs from the circuit The state In the previous section, the circuit events, cir1 and cir2, incremented directly the acknowledgement counters, a1 and a2.

These counters both formed the abstract outputs of our circuit. We shall now postpone this incrementation and have the circuit only generating an o set (that is, a 0 or a 1), the proper incrementation itself being done by the environment on two slightly time-shifted counters, say b1 and b2. But we want the circuit to produce boolean values only.

For this, we introduce a constant function b_2_01, transforming a boolean value into a numeric value.. axm1_1: b_2_01 BOO none none L {0, 1} constants: b_2_01 axm1_2: b_2_01(TRUE) = 1 axm1_3: b_2_01(FALSE) = 0. Development of electronic circuits This re nement intro none none duces thus four variables typed as follows:. inv1_1: b1 N inv1_2: o1 BOOL variables: b1, o1, b2, o2 inv1_3: b2 N inv1_4: o2 BOOL The gluing invaria none none nt that holds between the abstract counters a1 and a2 and the new concrete variables we have just introduced is the following:. inv1_5: mode = cir a1 = b1 inv1_6: mode = cir a2 = b2 inv1_7: mode = env a1 = b1 + b_2_01(o1) inv1_8: mode = env a2 = b2 + b_2_01(o2). The last two stateme none none nts indicate that, while we are observing the environment (just after the reaction of the circuit), the abstract counters ai are already incremented (by the abstract circuit), while the concrete counters bi are not. In fact, they will be incremented in the environment, thanks to the contents of the output oi. On the other hand, the rst two statements indicate that, while observing the circuit, the abstract and concrete counters are now in phase .

The events The environment events are all modi ed in a straightforward way: env1 when mode = env r1 = b1 + b_2_01(o1) then mode := cir r1 := r1 + 1 b1 := b1 + b_2_01(o1) b2 := b2 + b_2_01(o2) end env2 when mode = env r2 = b2 + b_2_01(o2) then mode := cir r2 := r2 + 1 b1 := b1 + b_2_01(o1) b2 := b2 + b_2_01(o2) end. 8.3 Second example: the arbiter env3 when mode = env r1 = b1 + b_2_01(o1) r2 = b2 + b_2_01(o2) then mode := cir r1 := r1 + 1 r2 := r2 + 1 b1 := b1 + b_2_01(o1) b2 := b2 + b_2_01(o2) end. The circuit events a none none re modi ed accordingly: cir1 when mode = cir r1 = b1 p2 = FALSE then mode := env o1 := TRUE o2 := FALSE p1 := FALSE p2 := bool(r2 = b2) end cir2 when mode = cir r2 = b2 p1 = FALSE then mode := env o1 := FALSE o2 := TRUE p1 := bool(r1 = b1) p2 := FALSE end. cir0 when mode = cir r1 = b1 r2 = b2 then mode := env o1 := FALSE o2 := FALSE p1 := FALSE p2 := FALSE end. Development of electronic circuits 8.3.4 Second re neme nt The state The environment events are now accessing environment variables only (r1, r2, b1, and b2) together with the outputs of the circuit (o1 and o2).

But, the circuit events still access the environment variables (r1, r2, b1, and b2). In this re nement, we introduce proper inputs i1 and i2 to the circuit. The inputs to the circuit, rather than being the number ri of requests and the number bi of acknowledgements could very well be only their di erence, which is at most 1, as we know from invariants inv0_5 to inv0_8.

For this, we introduce two new binary variables i1 and i2 :.
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