Direct feedback in asynchronous networks of input-output automata

Asynchronous automata networks are commonly used to describe discrete-event systems consisting of several components. The components used here behave asynchronously since this is usually the case for a large class of automation systems. The asynchronous behavior is based on the ability of certain components to change their state regardless of other component´s behavior in the network. This paper deals with the direct feedback problem which occurs whenever coupling input signals have an instantaneous effect on coupling output signals of the same component. In a loop of components the question arises whether a unique solution exists for the signal values in such a loop. A new well-posedness condition is proposed which can be used in composition and simulation algorithms. A CMOS-inverter is used as an example and results of computer simulation as well as the impact of the completeness of behavioral relations are discussed.