# Chapter 1: Regular Languages

## For Your Enjoyment

- A game that can be modeled with a finite automaton is
Manufactoria.

## Chapter 1.2, Nondeterminism

### Lecture Problem

- Problem: Design a nondeterministic finite automaton that accepts any binary
string that contains either 00 or 11.
- Theorem: The class of regular languages is closed under the
union operation.
- Prove the theorem by constructing NFA N from the union of NFA N
_{1}
and NFA N_{2}.
Let N_{1} =
(Q_{1}, Σ, δ_{1}, q_{1}, F_{1})
and N_{2} =
(Q_{2}, Σ, δ_{2}, q_{2}, F_{2}).

### Active Learning Problem

- Problem: Design a nondeterministic finite automaton that accepts any binary
string that contains the concatenation of 00 and 11.
- Theorem: The class of regular languages is closed under the
concatenation operation.
- Prove the theorm by constructing NFA N from the concatenation of
NFA N
_{1} and NFA N_{2}.

### Active Learning Problem

- Problem: Design a nondeterministic finite automaton that accepts the
language (101)*.
- Theorem: The class of regular languages is closed under the
star operation.
- Prove the theorem by constructing NFA N from the star of NFA N
_{1}.