Chomsky Normal Form

Duration: 6 min

This video lesson is available to enrolled students.

Return to /learn/NIACL-AO-IT-SPECIALIST/computer-architecture-it-specialist/grammar-cfg/normal-forms-bnf/asset-chomsky-normal-form after enrolling

Inside: a video lesson and guided study material.

Module outline

  1. Quantitative Aptitude: Ratio and Proportion (Ratios), Data Interpretation, Mixture and Alligation, Permutation and Combination, Number System, Sequence and Series (Series), Speed Time and Distance, Speed Mathematics and Basic Mathematics, Algebra, Percentage, Profit and Loss, Simple Interest and Compound Interest, Powers and Exponents (Surds and Indices), Time and Work, Mensuration and Geometry, Partnership
  2. Reasoning Ability: Series (Number and Letter Series) (Numerical Relations and Reasoning), Coding Decoding, Data Sufficiency, Seating Arrangements, Deductive and Inductive Reasoning (Logical Deduction and Induction) (Prepositional Reasoning), Directions (Direction Test), Ranking, Order and Sequence, Syllogisms, Blood Relations, Puzzle Solving (Puzzles), Inequality, Machine Input-Output
  3. English Language: Vocabulary, Noun, Subject Verb Agreement (Verb Noun Agreement), Adjectives, Tenses, Comprehension / Reading Comprehension / Unseen Passages (Critical Reasoning) (Paragraph Questions), Cloze Test (Cloze Passage), Sentence Correction (Error Correction), Sentence Completion (Fill in the blanks), Sentence Re-arrangements (Para Jumbles) (Narrative Sequencing), Sentence Construction, Pronoun, Preposition, Conjunction, Adverb, Verb, Modals, Articles, Determiner, Interjection
  4. General Awareness: Evolution of Indian Banking (Banking & Financial Awareness), GK- Current Affairs, Static General Knowledge, Indian Economy
  5. C Concepts + MCQs (IT Specialist): C Programming by Yash Sir, C Language Core
  6. Java (IT Specialist): Java
  7. Python (IT Specialist): Python for Placements by Yash Sir, Python Basics
  8. OOPs (IT Specialist): Object Oriented Programming (OOPS)
  9. DBMS (IT Specialist): Basics of DBMS, ER Diagram, Relational Model & Functional Dependencies, Keys & Integrity Constraints, Normalization (1NF - BCNF), Decomposition Properties & 4NF, File Organization & Indexing, Relational Algebra, Relational Calculus, Transaction Management, Concurrency Control, Database Recovery, ORDBMS, Database Security & Authorization, Query Processing & Optimization, Enhanced Data Models, Data Warehousing & Mining, Big Data Systems, NoSQL
  10. SQL (IT Specialist): SQL
  11. Software Engineering (IT Specialist): Fundamentals of Software Engineering, Software Requirements and Quality Assurance, Software Design, Estimation and Metrics, Software Testing, Software Maintenance and Configuration Management
  12. Data Structure (IT Specialist): Introduction to DS, Array, Stack, Queue, Linked List, Tree, Graphs, Hashing
  13. Operating System (IT Specialist): Introduction to OS, Process Management, CPU Scheduling, Process Synchronization, Deadlock, Threads & Process Creation, Memory Management, Virtual Memory, Disc Scheduling, File Management, Windows OS, Linux OS, Security, Distributed Systems, Virtual Machines
  14. Compiler Design (IT Specialist): Intro to Compilers, Lexical Analysis, Grammar & CFG, Syntax Analysis: Top-Down, Syntax Analysis: Bottom-Up, Semantic Analysis & SDT, Intermediate Code Gen, Code Optimization, Run Time Environment
  15. Computer Architecture (IT Specialist): Basics of COA, Floating Point Rep, Cache Memory Organization, Input Output Organisation, Pipelining, Instr Formats & Modes, Control Unit Design, Register Transfer and Microoperations, Multiprocessors, Programming the Basic Computer
  16. Data Communication & Networking (IT Specialist): Introduction to CN, Data Communication, DLL: Access Control, DLL: Flow Control, DLL: Error Control, DLL: Framing, Data Link Layer - Ethernet, Net Layer: IPv4 & Proto, Net Layer: IP Addressing, Net Layer:Routing Protocol, Transport Layer Services, TL: Congestion & UDP, Application Layer, Hardware basics, Network Security
  17. Descriptive Test (Main Exam): English Writing Ability
AI summary & chapters

AI Summary

An AI-generated summary of this video lecture.

The lecture introduces the concept of Normalization for Context-Free Grammars (CFG), specifically focusing on Chomsky Normal Form (CNF). The instructor defines CNF as a state where every production rule follows the format A → BC or A → a, where B and C are non-terminals and a is a terminal. The session transitions into a practical demonstration using the grammar S → aSb / ab. The instructor systematically converts this grammar into CNF by introducing auxiliary non-terminals to replace terminals and breaking down right-hand sides that exceed length two. Finally, the lecture concludes by deriving a mathematical property: for any string of length n derived from a CNF grammar, the number of production steps required is exactly 2n - 1.

Chapters

  1. 0:00 – 2:00 00:00-02:00

    The video begins with a slide titled 'Normalization of CFG'. The text defines Chomsky Normal Form, stating that a grammar G is in CNF if every production is in the form A → BC / a. Below this, the constraints are listed: B, C ∈ Vn (non-terminals) and a ∈ Σ (terminals). The instructor underlines the phrase 'Chomsky Normal Form' and uses red arrows to point to the components A, B, C, and a on the slide, emphasizing the structural requirements of the rule. He specifically highlights that B and C must be non-terminals from the set Vn, while a must be a terminal from the set Σ.

  2. 2:00 – 5:00 02:00-05:00

    The instructor moves to a whiteboard example with the production S → aSb / ab. He explains that this is not in CNF because the right-hand side contains terminals mixed with non-terminals and has a length of three. He introduces new non-terminals A and B with productions A → a and B → b. He rewrites the main rule as S → ASB / AB. Since ASB has length three, he introduces a new variable S1 (written as SA or similar) to split it, creating S1 → AS. The final normalized grammar is listed as S → S1 B / AB, S1 → AS, A → a, and B → b. He emphasizes that every rule must now strictly follow the A → BC or A → a format.

  3. 5:00 – 6:29 05:00-06:29

    The instructor discusses the relationship between string length and derivation steps. He writes |w| = n and states that for a CNF grammar, the number of productions needed is 2n - 1. He demonstrates this with a calculation: 2(4) - 1 = 7. He lists the sequence of sentential forms for a derivation of length 4: S, S1 B, ASB, aSB, aAB, aBb, ab. This confirms that there are exactly 7 steps, matching the formula. He circles the final string ab to show the result. The slide text reiterates that if a CFG is in CNF, the number of sentential forms for a string of length n is 2n - 1.

The lesson effectively bridges theory and practice. It begins by defining the rigid structural constraints of Chomsky Normal Form, ensuring productions are binary or unary. It then applies these constraints to normalize a specific grammar, demonstrating the necessary introduction of new variables to handle mixed terminals and long sequences. The session concludes by establishing a critical algorithmic property: the linear relationship between string length and derivation steps (2n - 1), which is fundamental for parsing algorithms like CYK.

Loading lesson…