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

# Equivalence of a nondeterministic vs. deterministic Turing machine
With the notion of encoding, we can show how to simulate a nondeterministic Turing machine (NTM) with a deterministic one. A **nondeterministic** Turing machine is one where there are multiple choices for combinations of current state and character:

\delta(q_i,c)=\{(q_{k_1},c_{k_1},D_{k_1}),(q_{k_2},c_{k_2},D_{k_2}),\cdots,(q_{k_n},c_{k_n},D_{k_n})\}

In other words, for $\text{NTM}$s, $\delta$ is a relation. To simulate an $\text{NTM}$ deterministically, we employ a breadth-first traversal of the tree of instantaneous descriptions representing all possible choices of applicable rules. Consider what happens at each step of an $\text{NTM}$, depicted by the sample graph below.

Learn how to simulate a nondeterministic Turing machine using a deterministic one.

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

Nondeterministic Turing machine = Deterministic Turing machine

Equivalence of a nondeterministic vs. deterministic Turing machine