We begin with a study of finite automata and the languages they can define (the so-called “regular languages.” Topics include deterministic and nondeterministic automata, regular expressions, and the equivalence of these language-defining mechanisms. We also look at closure properties of the regular languages, e.g., the fact that the union of two regular languages is also a regular language. We consider decision properties of regular languages, e.g., the fact that there is an algorithm to tell whether or not the language defined by two finite automata are the same language. Finally, we see the pumping lemma for regular languages – a way of proving that certain languages are not regular languages.

Our second topic is context-free grammars and their languages. We learn about parse trees and follow a pattern similar to that for finite automata: closure properties, decision properties, and a pumping lemma for context-free languages. We also introduce the pushdown automaton, whose nondeterministic version is equivalent in language-defining power to context-free grammars.

Next, we introduce the Turing machine, a kind of automaton that can define all the languages that can reasonably be said to be definable by any sort of computing device (the so-called “recursively enumerable languages”). We shall learn how “problems” (mathematical questions) can be expressed as languages. That lets us define problems to be “decidable” if their language can be defined by a Turing machine and “undecidable” if not. We shall see some basic undecidable problems, for example, it is undecidable whether the intersection of two context-free languages is empty.

Last, we look at the theory of intractable problems. These are problems that, while they are decidable, have almost certainly no algorithm that runs in time less than some exponential function of the size of their input. We meet the NP-complete problems, a large class of intractable problems. This class includes many of the hard combinatorial problems that have been assumed for decades or even centuries to require exponential time, and we learn that either none or all of these problems have polynomial-time algorithms. A common example of an NP-complete problem is SAT, the question of whether a Boolean expression has a truth-assignment to its variables that makes the expression itself true.

## Requirements

The primary prerequisite for this course is reasonable “mathematical sophistication.” That is, you should feel comfortable with mathematics and proofs. Specific topics that are useful include a knowledge of graphs, trees, and logic, as well as basic data structures and algorithms. If you do not meet the prerequisites, there is a free textbook, Foundations of Computer Science.

This list consists of the **Best Automata Theory Courses Online**. Our expert panel of reviewers have spent countless hours combing through the data and watching videos to create this list.

## 10 Best Automata Theory Online Courses

Course Name | Enrolled Students (Count) | Reviews (count) |
---|---|---|

1. Theory of Computation : Become a master of DFA Our Best Pick | 813+ | 95+ |

2. Theory of Automata | Theory of Computation & Formal Language | 326+ | 67+ |

3. Automata Theory | Theory of Computation Beginner to advanced | 240+ | 39+ |

4. Formal Languages and Automata theory | 47+ | 12+ |

5. Formal Languages & Finite State Automata: From the Beginning | 271+ | 11+ |

6. Theory of Computation (TOC) | 2928+ | 6+ |

7. Theory of Computation and Automata – Part 1 | 3500+ | 3+ |

8. Fundamentals of Automata Theory | 1782+ | 35+ |

9. Theory of computation from basics | 1229+ | 5+ |

10. Theory of Computation – Finite Automata | Automata Theory | 21+ | 3+ |

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This course provides a challenging introduction to some of the central ideas of theoretical computer science. Beginning in antiquity, the course will progress through finite automata, circuits and decision trees, Turing machines and computability, efficient algorithms and reducibility, the P versus NP problem, NP-completeness, the power of randomness, cryptography and one-way functions, computational learning theory, and quantum computing. It examines the classes of problems that can and cannot be solved by various kinds of machines. It tries to explain the key differences between computational models that affect their power.

Automata Theory is an exciting, theoretical branch of computer science. The word automaton itself, closely related to the word “automation”, denotes automatic processes carrying out the production of specific processes. Automata theory deals with the logic of computation with respect to simple machines, referred to as automata. Through automata, computer scientists are able to understand how machines compute functions and solve problems and more importantly, what it means for a function to be defined as computable or for a question to be described as decidable . Automatons are abstract models of machines that perform computations on an input by moving through a series of states or configurations. At each state of the computation, a transition function determines the next configuration on the basis of a finite portion of the present configuration. As a result, once the computation reaches an accepting configuration, it accepts that input. The most general and powerful automata is the Turing machine.