Overview

Last class:

• Regular expressions
• How can we use NFAs to compute regexes
• Regexes are DFAs/NFAs

Today:

• Limitations on automata

Summary on Automata

• NFAs
• DFAs
• Regexes

All equivalent

A function $f$ is regular if it is computable by a DFA or an NFA or a regex.

Programmers perspective: String matching, processing, single pass

Can DFAs compute everything?

What about the majority function? This is not regular, hence there is no DFA that can compute majority.

What about languages that contain an equal number of 0s and 1s? We still need to count.

$L_2=\{x:$ contains an equal number of $(01)$ and $(10) \}$

Interestingly, $L_2$ is regular.

$L_2=\{x:$ first and last bits are the same $\}$