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Explain the concept of strings in TOC?
A string over an alphabet is a finite sequence of letters from the alphabet.
Examples
toc, money, c, and adedwxq are strings over the alphabet ∑ = {a, b, c, . . . , z}.
84029 is a string over the alphabet ∑ = {0, 1, 2, . . . , 9}.
Empty String
The empty string or null string, denoted by ∧, is the string consisting of no letters, no matter what type of language we are considering.
String concatenation
Given two strings w1 and w2, we define the concatenation of w1 and w2 to be the string as w1w2.
Examples
If w1 = pq and w2 = r, then w1w2 = pqr.
If w1 = acc and w2 = ac, then w1w2 = accac and w2w1 = acacc.
If w1 = ∧ and w2 = cd, then w1w2 = cd.
If w1 = aa and w2 = ∧, then w1w2 = aa.
If w1 = ∧ and w2 = ∧, then w1w2 = ∧; because ∧∧ = ∧.
For any string w, we can define wn for n ≥ 0 inductively as follows −
w0 = ∧;
wn+1 = wnw for any n ≥ 0.
Example
If w = man, then w
0 = ∧, w
1 =mam, w
2 = mammam, w
3 = mammammam,
and so on.
Substring
Given a string s, substring of s is any part of the string s means w is a substring of s, if there exist strings x and y (either or both possibly null) such that s = xwy.
Examples
Take the string 472828. Then ∧, 282, 4, and 472828 are all substrings of 472828.
48 is not a substring of 472828.
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