In this paper, several aspects of the composition of discrete state condition/event systems according to Sreenivas and Krogh are discussed. We introduce a new composition operator called parallel interconnection. It is shown to be a generalization of the originally defined cascade and feedback operators. Based on this composition operator, a modular refinement rule is presented which can be use...

Given a description of the quantitative information flow (qif) for components, how can we determine the qif of a system composed from components? We explore this fundamental question mathematically and provide an answer based on a new composition operator. We investigate its properties and prove that it generalises existing composition operators. We illustrate the results with a fresh look on C...

We investigate requirements for a composition operator for complex control systems. The operator should be suitable for a context where we have both supervisory control and a system that consists of multiple (two or more) components. We conclude that using both passive (observing) and active (controlling) transitions is advantageous for the specification of supervisory control systems. We intro...

Let ǫ > 0. A continuous linear operator T : C(X) −→ C(Y ) is said to be ǫ-disjointness preserving if ‖(Tf)(Tg)‖ ∞ ≤ ǫ, whenever f, g ∈ C(X) satisfy ‖f‖ ∞ = ‖g‖ ∞ = 1 and fg ≡ 0. In this paper we address basically two main questions: 1.How close there must be a weighted composition operator to a given ǫ-disjointness preserving operator? 2.How far can the set of weighted composition operators be ...

Let H be a Hilbert space of analytic functions on the unit disk D. For an analytic function ψ on D, we can define the multiplication operator Mψ : f → ψf, f ∈ H. For an analytic selfmapping φ of D, the composition operator Cφ defined on H as Cφf f ◦ φ, f ∈ H. These operators are two classes of important operators in the study of operator theory in function spaces 1–3 . Furthermore, for ψ and φ,...