PRIORITIES AND INTERRUPTS

In this chapter will develop some additional features to the theory in the former chapters, in order to enlarge the area of its application. Let us start by introducing a mechanism to describe priorities in the system ACP of chapter 4 (see 4.2.1). In ACP with priorities some actions have priority over others in a sum. This mechanism can be used to model interrupts in a distributed system.

REMARK

We will not combine the system ACP with priorities with τ and the abstraction operator of chapter 5. This can be done in several ways, see 6.1.23.

PARTIAL ORDERING

Assume we have a partial ordering on the set of atomic actions A. This means that we have a relation < satisfying, for all a,b,c∈ A:

1. at most one< / i. of a < b, b < a, a = b is the case;

2. a<b and b<c imply a<c.

a<b now means that b has priority over a. Special constants like δ, are not included in the ordering, and thus never have priority over other actions (this is forced by axiom A6).

AIM

We want to define an operator ε implementing these priorities, i.e: if a<b, a<c, and b and c are not related, we want to have:

1. ε(a + b) = b; ε(a + c) = c;

2. ε(b + c) = b + c.

ACTION RELATIONS

It is relatively straightforward to give a definition by action relations of the priority operator. We present such a definition in table 68 below.