Formal Languages

These provide a convenient framework for analyzing decision problems.

An alphabet $\Sigma$ is a finite set of symbols.

A language L over $\Sigma$ is any set of strings made up of symbols in $\Sigma$.

Denote empty string $\epsilon$ and empty language $\emptyset$.

The language of all strings over $\Sigma$ is $\Sigma$*.
E.g., if $\Sigma$ = {0, 1}, $\Sigma$* = {$\epsilon$, 0, 1, 00, 01, 10, 11, 000, ..}