Fair controls and their realization

Abstract

The paper is based on the consideration of controls by restrictions of behaviour as introduced in [Bu]. Different notions of fairness and fair controls are derived from the fairness notions given in [LPS]: fairness is considered with or without reference to the behaviour of the original uncontrolled system, in connection with deadlock-avoidance (infinite fair controls) and by omitting termination caused by control (non-blocking), respectively. In general, not all fair execution sequences can be obtained by a single control. In this cases, each control can be replaced by a less restricting control. We give negessary and sufficient conditions for this fact. Different possibilities to realize controls by finite state mechanisms or by predefined delay functions are investigated. The control automata controlling arbitrary systems in a fair way are characterized. It turns out that the approach by control automata is preferable to the use of delay functions.