An Introduction to the Theory of Automata: Course Held at - download pdf or read online

By Fabrizio Luccio

ISBN-10: 321181082X

ISBN-13: 9783211810828

ISBN-10: 3709128161

ISBN-13: 9783709128169

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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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Application of input :x;n to A in state q~ is forbidden. Then that is, both next state and output are left unspecified. 2. Input Xn should never appear when A is in state qi. : if does appear, this corresponds to an quence. Then ~ :x;h in the input se- 5. , ö q may be extended as to include: o(q~' xh) = inserted in Q , and A. extended to: q. que output y , or a unique state q , may be emplied for all the non specifications of A due to error. 3. If input xh is applied to A in state q;, , it does not matter which one the next state or the output will be.

Then, every subclass of F is excluded by Fand need not be considered. The nurober of c-classes to be retained for selecting a minimal collection can be further reduced over the one of prime c-classes, if a technique for class set updating is used. Reducing the number of prime c-classes 51 In the above example, once the subclass {q 5 , qd has been excluded by F, the class set of E can be consequently updated. In fact, the closure requirement that q 5 and q6 be contained in the same class of the minimal collection, is now met by imposing the presence in such a collection of class {q 5 , q 6 , q,}, which is the only prime c-class containing; the above two states.

As already illustrated, the notion of equivalence is the key for comparison of the external behavior of complete automata, and ultimately for the minimization of a given complete automaton. However, if incompleteness is considered, it is not graph, indicating all the incorrect input alternatives from such a node, ( ~W<) 1\1\ The definition of applicable input sequence used here differs from the classical one. (See Ginsburg [3]. 1). 6. Inclusion 38 significant that two output sequences be equal in coincidence with unspecified elements.

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An Introduction to the Theory of Automata: Course Held at the Department for Automation and Information July 1971 by Fabrizio Luccio


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