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Extra info for An Introduction to the Theory of Automata: Course Held at the Department for Automation and Information July 1971

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And of size ~ , A in minimal form is observable in by performing an experiment of length -' n - 1 n- t, where n is the nurober of states of A • Then, for less powerful experiments than the one of Proposition 5, the automaton may not be observable even if it is in minimal form. For example, the following automaton (Arbib [5], Ch. 6): ( 15) 5. Incomplete automata 32 is in minimal form, but is not observable by simple experiments. In fact, no input sequence beginning with tween q 1 and q~ 1 1 can discriminate be- ; no input sequence beginning with :x:a.

In the definition of incomplete automata (section 5), the notion of unspecified next state was introduced: the transition to an unspecified state may be interpreted as the 7. Extensions 52 transition to any state. This concept may be further extended if, for any input-state pair, a subset of possible next states is specified. That is, A. g from Q x X onto a set of subsets of Q. An automaton with such a structure is called non determini- stic. Clearly, complete and incomplete automata are particular cases of non deterministic automata.

Consequently, "adjective 1" and "adjective 2" arealso compatible (proposition 7), and the compatibility classes of states are: {sentence}, {acephalous sentence {adjective 1, adjective z}' t}, {acephalous sentence 2} , {conjunction, terminator} ,{end}. Then, the following minimum state translator can be constructed (with obvious associations between -classes of (25)-(25 1 ) and states of (26): 6. Inclusion 48 I/io 2 am/sono (26) generous/ /generoso great/ /grande and/e ;/; Note that (26) is a finite automaton, which is able to accept input sequences of non finite length.

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