Technical Report CS0017

Title: Ultimate-Definite and Symetric-Definite
Authors: A. Paz and B. Peleg
Abstract: The present paper is concerned with a generalization of the definite automaton and definite event (see [K], [P, R &S], [B] ). In the next section we give the basic preliminary notions and definitions as well as a short account of known results relevant to our work. In sections 3, 4, 5 we introduce the notion of ultimate definite (u.d.) event and investigate the properties of this event in general. In Sections 6, 7 we treat regular u.d. events and give, in explicit form, an effective decision procedure whereby it can be decided whether a given finite automaton defines e u.d. event. In Section 8 we introduce the notion of reverse u.d. event and give a decision procedure for regular reveree u.d. events. Finally, in Section 9 we introduce the symmetric event, give an effective decision procedure for symmetric automata and introduce B canonical representation for this type of event.
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