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

By Fabrizio Luccio

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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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If (25) is completed by specifying the new outputs y = ERROR (as already donein (19)), no two states of the automaton are compatible. Hence, no state reduction for the translator is possible. Let us now further extend the input language, as to include conca~enations of adjectives of any length. Automaton (25) can be modified to process the new language, by including a transition between states "terminator" and "adjective 2", for input "and". med as: I I and/e 1 (25 ') generous/ /generoso great/ /grande In automaton (25)-(25') states "conjunction" and 11 terminator" are clearly compatible.

A minimal collection of c-classes is a complete and closed collection with minimum number of classes. 3. For any incomplete automatonA, an automaton A' with minimum number of states, such that A ~ A', can be constructed Assertion by associating the states of A' to the members of a minimal collection of c-classes of A. Inputs and outputs of A' are consequently assigned. 7. are respectively derived from {qu ql} and [q~}ยท (21) is still incomplete, although more densely specified than (20). However, also ' isaminimal collection for (20), and a second minimum state automaton that includes (20) can be derived.

In particular, any class containing exactly one state is a c-class. c-classes are relevant to the minimization problem, which will be solved through the selection of a proper collection of such classes. In order to discuss this point, some terminology is needed. For a given automaton A, a collection of c-classes is complete if every state of A is contained in at least one class of the collection. Given a c-class 6. Inclusion 42 let Ci. be the class of all the distinct specified sta tes among . , we say that Ci.

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