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

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9.5 A Computational Interleaving Semantics 271<br />

9.5 A Computational Interleaving Semantics<br />

9.5.1 Informal explanation<br />

The process-oriented part <strong>of</strong> POOSL will be formalised by means <strong>of</strong> a computational<br />

interleaving semantics. The semantics is specified by a labeled-transition system. A labeledtransition<br />

system is very similar to a ’normal’ transition system as described in Subsection<br />

8.5.1. It is represented by an ensemble (Conf p £<br />

a<br />

£ ¡ a ¡ Act¦ ) where Conf ¥ Act¥<br />

p is a<br />

set <strong>of</strong> configurations, Act is a set <strong>of</strong> atomic actions, and £<br />

¡ a<br />

¡ Act¦ a is a set <strong>of</strong> £ labeledtransition<br />

relations. If and S¥ I I¡ are configurations, then the intuitive meaning <strong>of</strong><br />

¥ S¡<br />

a<br />

<br />

£ S¡ ¥ I¡ is that a system S with an amount <strong>of</strong> information I can lead to system S¡<br />

S¥ I<br />

I¡ and information in a single transition step by performing atomic action a.<br />

The execution <strong>of</strong> a system <strong>of</strong> collaborating instances is modelled as the interleaving <strong>of</strong> all<br />

atomic actions, that is, as a sequential execution <strong>of</strong> these actions.<br />

9.5.2 Definitions<br />

The labeled-transition system will be based upon configurations <strong>of</strong> the form<br />

<br />

¥<br />

e<br />

¥ BSpec ¥ ¡ ¡<br />

1 ¥ ps1 ¥ n ¥ n psn Sys ¡ p Sys ¥<br />

Here BSpece denotes the system part (comparable to the statement (S) part<br />

<br />

in<br />

<br />

Subsection<br />

8.5.1) <strong>of</strong> ¡ ¡<br />

the ¥ configuration ¥ 1 and ¡ ¡ 1 ps1 , , ¡<br />

n ¥ n psn , ¡ Sys ¥ p and Sys together form<br />

the information part (the I part in Subsection 8.5.1 ).<br />

<br />

¡ 1 ¥¡ ¡ ¡ ¥<br />

<br />

BSpec e is an extended behaviour specification. The set B<strong>Specification</strong>s e denotes the set <strong>of</strong> all<br />

extended behaviour-specifications and is defined as<br />

BSpec e :: C p (E1 ¥¡ ¡ ¡ ¥ Er)<br />

¡ C c (E1 ¥¡ ¡ ¡ ¥ Er)<br />

¡ § S p£ e C p E1£ ¡ ¡ ¡ £ Er¢<br />

§ BSpec ¡ e C c ¡ ¡ ¡£ Er¢ E1£<br />

BSpec ¡ e 1 ¢ BSpece ¡<br />

2<br />

BSpece L<br />

BSpec ¡ e f §<br />

Cp ¥¡ ¡ ¡ ¥ (E1 Er) and Cc ¥¡ ¡ ¡ ¥ (E1 Er) denote an instance <strong>of</strong> some process class Cp ¥¡ ¡ ¡ ¥ yr y1<br />

and some cluster class Cc ¥¡ ¡ ¡ ¥ Pr P1 respectively, initialised to ¥¡ ¡ ¡ ¥ E1 § Er. Sp£ <br />

e<br />

Cp ¡ ¡ ¡£ Er¢ E1£<br />

denotes that extended process statement Sp£ e still has to be executed by process instance<br />

Cp ¥¡ ¡ ¡ ¥ (E1 § Er). BSpece C c ¡ ¡ ¡£ Er¢ indicates that behaviour expression BSpec E1£ e remains to<br />

be executed by cluster Cc ¥¡ ¡ ¡ ¥ (E1 Er). The other constructs denote parallel composition,<br />

channel hiding, and channel renaming respectively.<br />

¡<br />

¥ 1 ¥ 1 ps1 ¡ ¡ , , ¡ ¡<br />

¥ n ¥ n psn is a list <strong>of</strong> process environments, one for each ¡ initialised<br />

process object <strong>of</strong> BSpece . A process environment ¡<br />

ps¥ is composed <strong>of</strong> a variables<br />

¡ ¥<br />

state , a local process stack ps, and a type ¡ ¡ .

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