Regular Expressions - Stanford University
Regular Expressions
Recap from Last Time
Regular Languages
A language L is a regular language if there is a DFA D such that (D) = L.
Theorem: The following are equivalent:
L is a regular language. There is a DFA for L. There is an NFA for L.
Language Concatenation
If w * and x *, then wx is the concatenation of w and x.
If L and L are languages over , the concatenation of L and L is the language LL defned as LL = { wx | w L and x L }
Example: if L = { a, ba, bb } and L = { aa, bb }, then LL = { aaa, abb, baaa, babb, bbaa, bbbb }
Lots and Lots of Concatenation
Consider the language L = { aa, b } LL is the set of strings formed by concatenating pairs of
strings in L. { aaaa, aab, baa, bb }
LLL is the set of strings formed by concatenating triples of strings in L. { aaaaaa, aaaab, aabaa, aabb, baaaa, baab, bbaa, bbb}
LLLL is the set of strings formed by concatenating quadruples of strings in L. { aaaaaaaa, aaaaaab, aaaabaa, aaaabb, aabaaaa, aabaab, aabbaa, aabbb, baaaaaa, baaaab, baabaa, baabb, bbaaaa, bbaab, bbbaa, bbbb}
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