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Theory of Computation: Automata, Formal Languages, Computation and Complexity

Elevate your understanding of computer science with Theory of Computation and explore the mathematical foundations that define what computers can—and cannot—do.

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About This Course

Are you ready to move beyond just writing code and start understanding the mechanical limits of logic itself? The role of a high-level developer is evolving, requiring a deep grasp of Automata Theory, formal languages, and the efficiency of algorithms. This specialized course moves past simple syntax and dives into the abstract machines that power every compiler, search engine, and security protocol in use today.You will master the foundational models of computation, from simple Finite Automata to the universal power of Turing Machines. This program provides the logical rigor to distinguish between solvable problems and the mathematically impossible, giving you the edge in designing high-performance systems. 

Skills You’ll Get

  • Finite Automata & Regular Languages: Master the art of designing Deterministic and Non-deterministic Finite Automata (DFA and NFA). You will learn to apply Regular Expressions to solve lexical analysis problems and use the Pumping Lemma to prove the boundaries of regular languages.
  • Grammars & Pushdown Automata: Dive into the architecture of Context-Free Grammars. You will learn to build Pushdown Automata to handle recursive structures, a critical skill for understanding how modern programming languages are parsed and compiled.
  • Turing Machines & Computability: Explore the ultimate limits of logic with the Church-Turing Thesis. You will design Turing Machines to simulate any algorithmic process and tackle the famous Halting Problem to understand which computational tasks are truly "undecidable."
  • Computational Complexity & NP-Completeness: Master the classification of problems by their resource requirements. You will navigate the P vs. NP question, learn to use Polynomial-Time Reductions, and identify NP-Complete problems to ensure your software remains efficient and scalable.

Download Course Outline

1

Introduction

  • Significance of Theory
  • Background and Motivation
  • The Scope, Organization, and Approach
2

Mathematical Preliminaries

  • Introduction
  • Set Theory
  • Theorems and Proofs
  • Russell’s Paradox and Cantor’s Diagonal Argument
  • Set Relations
  • Functions
  • Graph Theory
  • Algebraic Theory of Machines
  • Operations on Strings
  • Strings and Languages
  • Closure Properties of Languages
  • Representation of Languages
  • Summary
3

Finite Automata and Regular Expressions

  • Introduction
  • Automata Theory
  • Modeling of Programs and Computation
  • Finite Automata Model
  • Regular Expressions
  • Applications of Finite Automata
  • Automata Concepts Through Games
  • Summary
4

Variants of Finite Automata

  • Introduction
  • Nondeterministic Finite Automata Model
  • Properties of NFA
  • Equivalence of NFA and DFA
  • Knowledge Check
  • Two-way Finite Automata
  • Knowledge Check
  • Finite Automata with Output
  • Equivalence of Moore and Mealy Machines
  • Knowledge Check
  • Finite-State Transducers
  • Knowledge Check
  • Summary
5

Minimization of Finite Automata

  • Introduction
  • Knowledge Check
  • From Regular Expression to DFA
  • Formalism for Minimization
  • Minimization of Finite Automata
  • Knowledge Check
  • NFA Homomorphism
  • Knowledge Check
  • State Minimization Based on Equivalence Classes
  • Knowledge Check
  • Myhill–Nerode Theorem
  • Knowledge Check
  • Partitioning State Space
  • Partition-Refine Algorithm
  • Table-filling Algorithm
  • Equivalences of Regular Expressions
  • Summary
6

Regular Languages

  • Introduction
  • Knolwedege Check
  • Regular Languages
  • Closure Properties of Regular Languages
  • On Regularity of Languages
  • DFA to Regular Expression
  • Pumping Lemma for Regular Languages
  • On Nonregularity of Languages
  • Myhill–Nerode Theorem and Its Applications
  • Regular Expression to DFA Using MN
  • Summary
7

Context-Free Grammars and Languages

  • Introduction
  • Context-Free Grammars
  • Relation Between FA and Regular Grammars
  • Derivation of Sentences
  • Closure Properties of Context-Free Languages
  • Parsing Context-Free Languages
  • Parsing Arithmetic Expressions
  • Ambiguous Grammars and Languages
  • Disambiguating Ambiguous Grammars
  • Operator-Precedence Grammars
  • Classifying Context-Free Grammars
  • Invertible Grammars
  • Summary
8

Normal Forms of Context-Free Grammars

  • Introduction
  • Simplification of Grammars
  • Chomsky Normal Form
  • Greibach Normal Form
  • Converting CNF to GNF Grammar
  • Complexity Analysis of GNF Grammar
  • Pumping Lemma for Context-Free Languages
  • Decidable Properties of Context-Free Languages
  • Summary
9

Pushdown Automata and Parsers

  • Introduction
  • The Idea of Parsing
  • Pushdown Automata Model
  • Formalism of PDA
  • Pushdown Automata Simulation
  • Types of PDAs
  • Language Acceptability by PDA
  • Equivalence of PDA and Context-Free Grammar
  • Parsers
  • LL(k) and LR(k) Grammars
  • LL Parser
  • LR Parser
  • Parallelization
  • Summary
10

Turing Machine and Computability

  • Introduction
  • Algorithmic Complexity
  • Analysis of Human Computation
  • Turing Machine Model
  • Language Recognition by Turing Machine
  • Turing Machines and Formal Languages
  • Computability
  • Church-Turing Thesis
  • Post Machine
  • Turing Machine Simulation
  • Computing Beyond the Turing Limit
  • Summary
11

Extensions of Basic Turing Machine

  • Introduction
  • Multi-tape Turing Machine
  • Linear Speedup
  • Multiple-track Turing Machine
  • Nondeterministic Turing Machine
  • Turing Machine and Type-0 Grammars
  • Universal Turing Machine
  • The Halting Problem of TM
  • Modern Computer Simulation on Turing Machine
  • Computing Frameworks
  • Summary
12

Linear-Bounded Automata and Context-Sensitive Languages

  • Introduction
  • Linear-Bounded Automata Model
  • Language Acceptability by LBA
  • Context-Sensitive Grammars and Languages
  • Non-context-free Properties of Programming Languages
  • Chomsky-Hierarchy Grammars and Languages
  • Closure Properties of Context-Sensitive Languages
  • Indexed Grammars
  • Regulated Rewriting Grammars
  • Knowledge Check
  • Conjunctive Grammars
  • Universal Versus Chomskian Grammars
  • Summary
13

Decidability, Undecidability, and Unsolvability

  • Introduction
  • Recursive and Recursive Enumerable Sets
  • Computable Sets
  • Recursive and Recursively Enumerable Languages
  • Decision Problems
  • Some Standard Problems and Their Intuitive Algorithms
  • Decidable Properties of Grammars and Languages
  • Enumeration of Languages and Turing Machines
  • Gödel Numbering
  • Knowledge Check
  • Knowledge Check
  • Unsolvability
  • Undecidability
  • Undecidability of Halting Problem
  • Rice’s Theorem
  • Summary
14

Computational Complexity Theory

  • Introduction
  • Determining Time Complexity
  • Time Complexity of Arithmetic Operations
  • Multi-tape Turing Machine Complexity
  • Concepts of Time and Space Complexities
  • Computational Complexity
  • Time- and Space-Bounded Complexities
  • Time-Bounded Complexity Classes
  • Knowledge Check
  • Space-Bounded Complexity Classes
  • Canonical Complexity Classes
  • Circuit Complexity
  • Reducibility
  • Primality and Compositness
  • Summary
15

NP-Completeness

  • Introduction
  • Class NP
  • Knowledge Check
  • Boolean Satisfiability
  • Cook–Levin Theorem
  • NP-Completeness
  • NP-Complete Problems
  • Solving SAT Problems
  • Counting Problems
  • Summary

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This program is ideal for computer science students and software engineers who want to understand the mathematical "why" behind computing. It is essential for anyone aiming to work in compiler design, cryptography, or advanced system optimization.

We cover the core of Computational Complexity, teaching you how to classify problems into P, NP, and NP-Complete classes, while exploring why the P vs. NP question remains the most important unsolved mystery in computer science.

Yes. While the core is theoretical, we bridge the gap by showing how Regular Expressions and Context-Free Grammars are the building blocks of modern compilers, text processing tools, and pattern-matching algorithms.

The primary focus is on Theory of Computation and mathematical modeling. However, you will engage in hands-on labs where you construct state diagrams and simulate machine behavior, ensuring you can visualize how these abstract concepts translate into computational reality.

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  Join our Theory of Computation program today to master the logical foundations that drive the future of technology.

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