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Specification of Reactive Hardware/Software Systems - Electronic ...

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290 Process Part <strong>of</strong> POOSL<br />

initial method call start<br />

instance methods ¡ start ¡ dB<br />

in?receive(dB); out!deliver(dB); start<br />

A transition graph <strong>of</strong> the buffer is given in Figure 9.4. The (parameterised) configurations<br />

are given by<br />

where<br />

conf p'<br />

1<br />

conf p'<br />

5<br />

(γ)<br />

τ<br />

a!<br />

conf p'<br />

2<br />

τ<br />

conf p'<br />

4<br />

(γ)<br />

τ<br />

a?<br />

conf p'<br />

3<br />

Figure 9.4: A Transition Graph <strong>of</strong> the 1-place Buffer<br />

conf p<br />

1 ¡ <br />

¥ Sys Buffer¥ p Sys ¡ ¥<br />

conf p<br />

<br />

Buffer ¥ envB ¥ Sys § start p Sys ¥ ¡<br />

conf p<br />

2 ¡ <br />

3 ¡ <br />

§ start (in?receive(dB); start) out!deliver(dB); ¥<br />

Buffer<br />

¥ Sys envB(nil) p ¥ Sys ¡<br />

conf p<br />

4 ¡ <br />

§ ( ) start <br />

(out!deliver(dB); ¥ Buffer ) ¥<br />

p envB( ¡ ¥ Sys Sys start)<br />

conf p<br />

5 ¡ <br />

§ ( ) start <br />

¥ Buffer ) ¥<br />

p envB( ¡ ¥ Sys Sys (start)<br />

<br />

£<br />

¦ ¥ ¥ ¤ <br />

envB proc £<br />

£ £ ¤<br />

¤ ¦ ¥ proc¥<br />

envB( £ ¦ ¥ ¤ <br />

) proc dS £<br />

It is not hard to verify that relation defined by<br />

with<br />

A<br />

B<br />

C<br />

D<br />

(A B) ¦ (C D)<br />

conf p<br />

1<br />

¥¡ ¡ ¡ ¥ conf p<br />

5<br />

¥ conf p<br />

8<br />

p p<br />

conf ¥ 9 conf ¦ ¦ 11 ¥<br />

£<br />

£<br />

conf p<br />

p<br />

p<br />

p<br />

14( )¥ conf15( )¥ conf16( )¥ conf<br />

£<br />

conf p<br />

1 ¡ conf ¥ p<br />

2 ¡ conf ¥ p<br />

3 ¡ conf ¥ p<br />

5 ¡ £<br />

¦<br />

conf p<br />

p<br />

p<br />

10( )¥ conf12( )¥ conf<br />

£<br />

conf p<br />

4 ¡ ¦<br />

17( ) ¡ ¡ PDObj¦<br />

13( ) ¡ ¡ PDObj¦ ¦<br />

£<br />

conf p<br />

18( ¥¡ ) ¡ ¥¡ ¡ PDObj¦

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