Gain insights into formal languages, regular languages, regular expressions, context-free languages, and Turing machines. Delve into automata models and enhance problem-solving skills through extensive exercises.

What are the mathematics behind computers? What are the theoretical foundations of computer languages? Such questions can be explored by understanding formal languages and automata models. 

In this comprehensive course, you’ll explore formal languages, regular languages, and how to model them with their associated automata models. Next, you’ll cover regular expressions and grammar, and their equivalents. Then, you’ll explore context-free languages (the foundations of programming languages), pushdown automata, and the relationship between them. Toward the end, you’ll learn about recursively enumerable languages, Turing machines with their variations, context-sensitive languages, and unrestricted grammars.

By the end of the course, you’ll have gained a deep understanding of several formal languages and their associated automata. Also, since there are plenty of exercises throughout the course, your understanding and problem-solving skills will be thoroughly reinforced.

Theory of Computation

The concepts of a start state, accepting state, and changing state depending on input stimuli can also be found in many real-life scenarios: scoring a tennis game, modeling a vending machine, or opening and closing an automatic door. All of them can be depicted using "state machines" as discussed below.

# Scoring a tennis game
The machine in the figure below illustrates how to score a tennis game. Each time a player wins a volley, the score progresses through the following point-level sequence: love (0), 15, 30, 40, game. When the score is tied 40--40, it is called a **deuce**. To win the game from deuce, a player must win two volleys in a row. Winning the first volley from the deuce gives the player the "advantage," but that player must win the very next volley to win the game. Otherwise, the play returns to deuce. This could go on for some time.  Observe the cycles between the *Deuce* state and the advantage states *Ad-S*  and *Ad-O* in the figure below.

Learn about some real-life applications of finite automata.

Getting Started

Exam on Formal Languages

Finite Automata

Exam on Finite Automata

Regular Expressions and Grammars

Exam on Regular Expressions and Grammars

Properties of Regular Languages

Exam on Properties of Regular Languages

Pushdown Automata

Exam on Pushdown Automata

Context-Free Grammars

Exam on Context-Free Grammars

Properties of Context-Free Languages

Exam on Properties of Context-Free Languages

Turing Machines

Exam on Turing Machines

The Landscape of Formal Languages

Exam on the Landscape of Formal Languages

Computability

Exam on Computability

Conclusion

Finite Automata in Real-life Situations

Scoring a tennis game