A Complete Inference System for a Class of Regular Behaviours

Let us think of such a tree (in which we take no account of the order among the sons of a node) as modelling the behaviour of a machine accepting symbols from, or submitting to observations by, its environment. In tree Tl only the symbol a may be accepted at the start (or, only the observation a may be made), after which b or c may be accepted. The tree is determinate, since no node has two outgoing arcs with the same label. In T2 the same is true at the start, but the tree (or the machine modelled) is not determinate. Factors beyond the observer’s control or knowledge will determine whether it is only b, or only c, which may be observed after the observation of a. Borrowing a phrase from C. A. Petri, we may think of information entering the observed system at different points in time-specifically, at each nondeterminate node of the tree. This information may be, for example, the influence of ambient temperature. Alternatively, tree T2 may be a model suitable for an observer with imperfect vision, in that he cannot see a difference between actions a, and a,, but takes them both to be a. For a better observer, the determinate tree T3 may be a better model. But even the first observer can discover that the machine modelled by Tl is different 439 0022-0000/84 $3.00