On the Minimality of Stream X-machines

One approach to formally specifying a system is to use a form of extended finite-state machine called a stream X-machine. A stream X-machine is a type of X-machine that describes a system as a finite set of states, each with an internal store, called memory, and a number of transitions between the states. A stream X-machine may be modelled by a finite automaton (the associated finite automaton) in which the arcs are labelled by function names (the processing functions). One important problem that may appear in the specification process is to find a ‘minimal’ (in some sense) stream X-machine that specifies the required functionality. This paper investigates the minimality issue in the context of deterministic stream X-machines and considers two types of minimality: state-minimal stream X-machine with respect to and minimal cover with respect to , where is the set of processing functions that the machine may use.