Ultimate-Definite and Symmetric-Definite Events and Automata

Abstract

New classes of events and finite automata which generalize the noninitial definite class are introduced. These events, called “ultimate definite” (u.d.), “reverse u.d.” and “symmetric definite,” are investigated as to algebraic and closure properties. Effective decision procedures whereby it can be decided whether a given finite automata defines such an event are given and unique canonical representations for these events are derived.