Download Applied Automata Theory by Julius T. Tou (Eds.) PDF

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By Julius T. Tou (Eds.)

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B. (x, *■') as before. b. (x, π') is the partition on S 3 a and b Ç the same block of π ΓΛ π' «=> a and 6 Ç same block of ττ and also Ç the same block of π'. For example, if S = {1, 2, 3, 4, 5, 6, 7, 8, 9}, { 1 , 2 , 3 , 4 ; V 6 ; 7 7 8 7 9 } Π {ΪΤ^Γδ; 3 7 ^ 7 ; 6; 8~9} = {Ϊ72;Μ;5;6;7;8~9}. b. (τ, π') is the partition on S ^ a and 6 Ç the same block of π U π' <=> 3 a finite sequence a = s0, s i , s 2 , · · ·, Sk-i, Sk = b of elements of £ 9 s» and s i+ i Ç the same block of π or to the same block of π'.

AN INTRODUCTION TO REGULAR EXPRESSIONS FIG. 45 4. the prevalence and the obvious theoretical usefulness of nondeterministic concepts cannot be denied; rather, we are left with a challenge to explain why it is that these concepts are useful. In this case, we are interested in the nondeterministic machine only as a way of describing a set, namely, the set of all words that could be generated. Thus, there is no sense in building such a machine, since the regular expression is as concrete as we have to get.

Then if you throw away another symbol, you are left with a word of length 1, a single symbol. When you throw away that symbol, you are left with a word of zero length, the null word. The concept of the null word turns out to be important because of the manner in which it concatenates with other words: thus, for any W, \W = W\ = W. As a consequence, for any set a, αλ = λα = a. This behavior of the null word is almost its definition. By the way, we see in the notation "λα" a tendency that may tend to dismay the logical purist, but is convenient in the practice of writing regular expressions.

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