An Introduction to the Theory of Automata: Course Held at by Fabrizio Luccio

By Fabrizio Luccio

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The relation of inclusion can be extended to automata. Definition 14. Automaten P is included by automaton 5 if and only if for each sta te p of P there is a sta te s of 5 , such that p ~ s . In symbols, the inclusion between automata is still indicated as P' S. Its intuitive meaning is that S performs any task that P does. Such a relation is of crucial importance for the minimization problem. In fact, for an incomplete automatonA the above problern can be formulated as the one of finding an automaton A' wi th minimal nurober of sta tes, such tha t A ~ A'.

54 7. Extensions A second field worth to be investigated is the one of controllability and observability for incomplete and non deterministic automata. Finally, a very interesting extension is to remove the assumption for the automaton to be stationary (section 2), to study the theory of automata wtih variable structure. A. Arbib. Theories of abstract automata. Prentice Hall, Englewood Cliffs, 1969. [2] R. Bellman and s. Dreyfus. Applied dynamic Prograrnming. Princeton University Press, Princeton, 1962 [3] s.

The relation of inclusion can be extended to automata. Definition 14. Automaten P is included by automaton 5 if and only if for each sta te p of P there is a sta te s of 5 , such that p ~ s . In symbols, the inclusion between automata is still indicated as P' S. Its intuitive meaning is that S performs any task that P does. Such a relation is of crucial importance for the minimization problem. In fact, for an incomplete automatonA the above problern can be formulated as the one of finding an automaton A' wi th minimal nurober of sta tes, such tha t A ~ A'.

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