Welcome to the world of Automata and Regular Languages!
This page is your gateway to understanding how machines recognize and describe regular patterns in computation. You’ll move step by step — from basic definitions of automata and regular expressions to algorithms, constructions, and key properties — all explained with clear examples and intuition-driven insights.
Prerequisites
To get the most out of these lessons, you should be familiar with some basic concepts from discrete mathematics, such as sets, functions, counting, relations, etc.
Whenever we use a concept from discrete math, we will:
- Provide intuition and examples so you can follow without getting lost.
- Explicitly define it or link to a reference.
Lessons
Links to Lessons:
1
Alphabets, Words, and Languages
This lesson introduces the fundamental building blocks of automata and formal languages. We cover alphabets, words, and languages, explaining how words are formed from finite sets of symbols and what languages are. Key operations on words (concatenation, powers, prefixes, suffixes, infixes) and on languages (union, intersection, difference, complement, concatenation) are defined and illustrated with examples. These concepts are essential for studying deterministic finite automata (DFAs) in subsequent lessons.
2
What Is a Deterministic Finite Automaton?
This lesson introduces deterministic finite automata (DFAs), a fundamental computational model. We start with an example — a digital safe box — to illustrate how DFAs process inputs step by step. The lesson then formalizes the concepts of states, transitions, runs, and acceptance, leading to the definition of the language recognized by a DFA. Finally, we define regular languages as those recognized by DFAs and provide an example showing how automata capture concrete patterns. By the end of the lesson, readers will understand both what a DFA is and how it recognizes a language, preparing them for designing and analyzing automata in subsequent lessons.