Automata Theory
Automata theory is the study of abstract machines and the problems they can solve. These abstract machines, called automata, are mathematical models of computation that define classes of problems that can be solved using different types of computational resources.
By studying automata, we can understand the fundamental capabilities and limitations of computation, laying the groundwork for important concepts in computer science such as parsing, compilers, and computational complexity.
Topics
1. Alphabets, Strings, and Languages
Learn the fundamental building blocks of formal languages: alphabets, strings, and the mathematical concept of a language.
Study This Section2. Deterministic Finite Automata (DFAs)
Study the simplest model of computation capable of recognizing regular languages.
Study This Section3. Nondeterministic Finite Automata (NFAs)
Explore a more flexible model of computation that is equivalent in power to DFAs.
Study This Section4. Regular Expressions
Learn a concise notation for describing regular languages and its connection to finite automata.
Study This Section5. Properties of Regular Languages
Understand closure properties and techniques for proving that a language is not regular.
Study This Section6. Context-Free Grammars and Languages
Move beyond regular languages to express nested structures like balanced parentheses and simple programming language syntax.
Study This Section7. Pushdown Automata (PDAs)
Study computational models with a stack that can recognize context-free languages.
Study This Section8. Turing Machines and Computability
Explore the most powerful model of computation and its implications for what can be computed.
Study This SectionApplications
Compiler Design
Automata theory is foundational for lexical analysis, syntax analysis, and parsing in compiler construction.
Text Processing
Regular expressions are used extensively in pattern matching, text search, and lexical analysis.
Formal Verification
Automata-based methods can verify correctness of protocols, hardware designs, and software systems.
Natural Language Processing
Context-free grammars help model syntactic structures in human languages.