On the Minimality of Finite Automata and Stream X-machines for Finite Languages

A cover automaton of a finite language L is a finite automaton that accepts all words in L and possibly other words that are longer than any word in L. An algorithm for constructing a minimal cover automaton of a finite language L is given in a recent paper. This paper goes a step further by proposing a procedure for constructing all minimal cover automata of a given finite language L. The concept of cover automaton is then generalized to a form of extended finite automaton, the stream X-machine, and the procedure is extended to this more general model.