Deterministic Generalized Automata

A generalized automaton (GA) is a nite automaton where the single transitions are deened on words rather than on single letters. Generalized automata were considered by K. Hashiguchi who proved that the problem of calculating the size of a minimal GA is decidable. We deene the model of deterministic generalized automaton (DGA) and study the problem of its minimization. A DGA has the restriction that, for each state, the sets of words corresponding to the transitions of that state are preex sets. We solve the problem of calculating the number of states of a minimal DGA for a given language, by giving a procedure that eeectively constructs a minimal DGA starting from the minimal equivalent (conventional) deterministic automaton.