# Chapter 1: Regular Languages

• 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 N1 and NFA N2. Let N1 = (Q1, Σ, δ1, q1, F1) and N2 = (Q2, Σ, δ2, q2, F2).

### 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 N1 and NFA N2.

### 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 N1.