By Julius T. Tou (Eds.)

ISBN-10: 1483200167

ISBN-13: 9781483200163

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**Extra info for Applied Automata Theory**

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7 that { [ ( 0 U 1)*000]*001J* = ( 0 U 1)*000001(001)*U (001)*; Fig. 8 that [(1*0)*01*]* = X U 0 ( 0 U 1 ) * U ( 0 U 1 ) * 0 0 ( 0 U 1 ) * . ) Note that, in these graphs, branches are labeled with arbitrary words instead of just letters of the alphabet; this practice makes them easier to draw and easier to look at. The reader who studies Figs. 6-8 will naturally ask the question, is there a set of formal rules for graph manipulation of this kind? As far as I know, no one has put forth a set of rules that are valid, simple, formally precise, and complete.

0 1 0. When the input is r 2 , the state matrix is Po(r2) = "0 1 0" 0 1 0 1 0 0 This concept of representation will be used in the study of unreliable finite automata in later sections. Certain automata have the property that starting with any state Xi we may transform the automaton into any other state xj through an appropriate sequence of input alphabets. Such automaton is referred to as a strongly connected machine. The major problems in the study of automata are the analysis of the transition and output responses of a given machine, the reduction of given machines to simpler machines (for instance, minimum machines) which are in some sense equivalent, and the synthesis or construction of machines having specified response characteristics for information processing.

And, for further clarification of this point, note that for each well-formed part of the regular expression [0(11) * U 10]* there is a corresponding part of the graph, in such a way that if one well-formed part of a regular expression is part of another, the same is true of the corresponding part of the graph. Hopefully, the notion of structure of regular expressions and graphs is clear. Then the point is that, although every regular expression has a graph that represents the same event and has the same, or almost the same, structure, there are some graphs whose structures are very far from the structure of any regular expression.

### Applied Automata Theory by Julius T. Tou (Eds.)

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