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 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.

In-Class Notes