Practice Problem on First Function

Duration: 8 min

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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.

This educational video provides a detailed lecture on Compiler Design, specifically focusing on the calculation of First and Follow sets for context-free grammars. The instructor systematically works through multiple examples of increasing complexity, demonstrating how to derive these sets for various production rules. The session begins with simple recursive grammars involving epsilon productions and progresses to standard arithmetic expression grammars. The lecture concludes with a theoretical overview of the formal rules used to calculate First sets for both terminals and non-terminals.

Chapters

  1. 0:00 – 2:00 00:00-02:00

    The instructor begins with a grammar: S -> AaB / Bb, A -> bA / epsilon, B -> cB / epsilon. He calculates First(A) as {b, epsilon} and First(B) as {c, epsilon}. For First(S), he analyzes the productions S -> AaB and S -> Bb. Since A can derive epsilon, 'a' is added to First(S). Since B can derive epsilon, 'b' is added. The final set written on the board is First(S) = {b, a, c}. He then transitions to a second example: S -> AB, A -> a / epsilon, B -> b / epsilon. He determines First(A) = {a, epsilon} and First(B) = {b, epsilon}. He explains that First(S) becomes {a, b, epsilon} because both A and B can derive epsilon, allowing the derivation to continue or terminate early.

  2. 2:00 – 5:00 02:00-05:00

    The lecture progresses to a more complex chain: S -> ABCDE. The non-terminals A, B, C, and E have epsilon productions (A -> a/epsilon, B -> b/epsilon, C -> c/epsilon, E -> e/epsilon), while D -> d is a terminal production. The instructor calculates First(A)={a, epsilon}, First(B)={b, epsilon}, First(C)={c, epsilon}, First(D)={d}, and First(E)={e, epsilon}. He determines First(S) = {a, b, c, d} because the derivation stops at D. Next, he analyzes S -> aAB / BA, A -> BA / epsilon, B -> AB / a / epsilon. He finds First(B) = {a, epsilon} and First(A) = {a, epsilon}. Consequently, First(S) is derived as {a, epsilon} based on the union of the first symbols of the productions.

  3. 5:00 – 8:28 05:00-08:28

    The instructor presents S -> AA, A -> aA, A -> b. He calculates First(S) = {a, b} and First(A) = {a, b}. He then moves to a list grammar: S -> (L) / a, L -> SL', L' -> ,SL' / epsilon. He calculates First(L') = {,, epsilon}. He then tackles a standard arithmetic expression grammar: E -> TE', E' -> +TE' / epsilon, T -> FT', T' -> *FT' / epsilon, F -> (E) / id. He calculates First(F) = {(, id}, First(T') = {*, epsilon}, First(T) = {(, id}, First(E') = {+, epsilon}, and First(E) = {(, id}. Finally, he shows a slide defining the rules for First(alpha), covering terminals, epsilon productions, and sequences of non-terminals, explaining that First(alpha) is the set of all terminals that may begin in any sentential form derived from alpha.

The video effectively bridges practical examples with theoretical definitions. By starting with simple recursive structures and moving to complex chains and standard expression grammars, the instructor demonstrates the iterative nature of First set calculation. The final slide reinforces the logic used throughout the examples, providing a formal framework for students to apply to new problems. The progression from specific calculations to general rules ensures a comprehensive understanding of the topic.

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