Seventh Lecture -- Patterns and Regular Expressions October 9, 2006
Patterns (look at definition in Kozen.)
Regular expressions (look at definitions in Kozen.)
If you are familiar with this, the "regular expressions" of perl
are the regular expressions of ours. If you are really familiar with
perl, think of the differences (are there any?)
Theorem: Languages denoted bt regular expressions are regular
Proof: these languages are regular (by the inductive definition.) The other
direction has a proof similar to the dynamic programming algorithm for shortest
paths (details next lecture.)