Languages and Regular expressions - University of Illinois Urbana-Champaign
Languages and Regular expressions
Lecture 2
1
Strings, Sets of Strings, Sets of Sets of Strings...
? We defined strings in the last lecture, and showed some properties.
? What about sets of strings?
2
CS 374
n, *, and +
? n is the set of all strings over of length exactly n. Defined inductively as: ? 0 = {} ? n = n-1 if n > 0
? * is the set of all finite length strings: * = n0 n
? + is the set of all nonempty finite length strings: + = n1 n
3
CS 374
n, *, and +
? |n| = ?||n ? |?n| = ?
? ?0 = {} ? ?n = ??n-1 = ? if n > 0 ? |?n| = 1 if n = 0 |?n| = 0 if n > 0
4
CS 374
n, *, and +
? |*| = ?
? Infinity. More precisely, 0
? |*| = |+| = |N| = 0 ? How long is the longest string in *?
no longest string!
? How many infinitely long strings in *? none
CS 374
5
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