Overview

Last time:

• Convert NFAs to DFAs
• Can implement NFAs easily

Today:

• Regular expressions
• Application of NFAs

Regular Expressions

Let’s say we want to find some pattern $p$ (bit string) in some text $x$.

Question: Does $p$ occur in $x$? If yes, can you find where?

Naive solution: $\mathcal{O}(mn)$

Famous algorithm: Knuth-Morris-Pratt (KMP)

Solves string matching in time $\mathcal{O}(n+m)$

• Given $p$, it constructs a DFA $D$ on $m+1$ states
• This $D$ has property for any string $y$, $p$ occurs in $y$ $\iff D(y) = 1$

Fragile X Syndrome

Take some DNA sequence $\{A,G,C,T\}^*$. A person has this syndrome if the following is present in their DNA: $GCG(CGG|AGG)^+AGG$