# Lecture Notes on Automata, Languages, and Grammars

## TL;DR

These lecture notes provide an accessible overview of automata theory, exploring deterministic and nondeterministic computation, correcting historical misconceptions, and discussing advanced topics like counter automata and algebraic generating functions.

## Contribution

The notes clarify the relationship between determinism and nondeterminism in automata and restore the importance of the Myhill-Nerode theorem in automata theory.

## Key findings

- Nondeterminism is equivalent to determinism in finite automata.
- Restoration of the Myhill-Nerode theorem's significance.
- Discussion of advanced automata models and their properties.

## Abstract

These lecture notes are intended as a supplement to Moore and Mertens' The Nature of Computation or as a standalone resource, and are available to anyone who wants to use them. Comments are welcome, and please let me know if you use these notes in a course. There are 61 exercises. I emphasize that automata are elementary playgrounds where we can explore the issues of deterministic and nondeterministic computation. Unlike P vs. NP, we can prove that nondeterminism is equivalent to determinism, or strictly more powerful than determinism, in finite-state and push-down automata respectively. I also correct several historical and aesthetic injustices: in particular, the Myhill-Nerode theorem and the idea of building minimal DFAs from equivalence classes of prefixes is restored to its rightful place above the Pumping Lemma for regular languages. I also discuss the Pumping Lemma for context-free languages, and briefly discuss counter automata, queue automata, and the connection between unambiguous context-free languages and algebraic generating functions.