Practice Problem on First Function

Duration: 8 min

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Inside: a video lesson and guided study material.

Module outline

  1. About the Course: About the Course
  2. Section 1 | Language (Hindi): भाषा, लिपि, ध्वनि, वर्ण, अक्षर, स्वर, व्यंजन, मात्रा और संयुक्ताक्षर, वर्तनी, वर्ण-विन्यास, अनुस्वार, अनुनासिक, चंद्रबिंदु और ‘र’ के रूप, शब्द, पद और शब्द-भेद, संज्ञा और सर्वनाम, विशेषण और क्रिया, लिंग, वचन, पुरुष और कारक, काल, वाच्य, वाक्य और वाक्य-भेद, संधि, समास, विलोम शब्द, पर्यायवाची शब्द, सामान्य अशुद्धियाँ, अनेक शब्दों के लिए एक शब्द, मुहावरे और लोकोक्तियाँ, अपठित गद्यांश और अपठित पद्यांश, Multi-Topic Content (Cross-Concept Material), वर्णमाला
  3. Section 1 | Language (उर्दू भाषा — 22 प्रश्न (निश्चित)): Spelling & Diacritics, Grammar (اسم, فعل, صفت, ضمیر), Vocabulary, Idioms & Proverbs, Comprehension
  4. Section 1 | Language (বাংলা / बांग्ला भाषा — 22 प्रश्न (निश्चित)): Bangla Script and Sounds, Bangla Grammar and Usage, Bangla Word Formation and Vocabulary, Reading and Text Interpretation
  5. Section 1 | Language (English): Vocabulary, Noun, Subject Verb Agreement (Verb Noun Agreement), Adjectives, Tenses, Pronoun, Verb, Adverb, Preposition, Articles, Determiner, Conjunction, Modals, Active Passive Voice (Voice), Direct and Indirect Speech, Sentence Correction (Error Correction), Sentence Completion (Fill in the blanks), Sentence Construction, Sentence Re-arrangements (Para Jumbles) (Narrative Sequencing), Comprehension / Reading Comprehension / Unseen Passages (Critical Reasoning) (Paragraph Questions), Cloze Test (Cloze Passage), Verbal Analogy (Word Based Analogy), Facts, Inference and Judgements
  6. Section 2 | Primary Maths & Reasoning: Ratio and Proportion (Ratios), Divisibility Rules, Mixture and Alligation, Permutation and Combination, Number System, HCF LCM, Sequence and Series (Series), Speed Time and Distance, Series (Number and Letter Series) (Numerical Relations and Reasoning), Coding Decoding, Non Verbal Reasoning (Spatial Aptitude) (Spatial Reasoning) (Visual Reasoning), Percentage, Average, Profit and Loss, Simple Interest and Compound Interest, Time and Work, Mensuration and Geometry, Age Problems, Arithmetic, Powers and Exponents (Surds and Indices), Algebra, Probability, Trigonometry, Syllogisms, Seating Arrangements, Blood Relations, Directions (Direction Test), Analytical Reasoning (Counting Figures Reasoning), Puzzle Solving (Puzzles), Calendar, Clock, Cubes & Dices, Venn Diagram, Data Arrangement, Inequality, Analogy, Ranking, Order and Sequence
  7. Section 2 | General Awareness (GK + Current Affairs): Polity, Physics, Biology, State Wise GK, Chemistry, History, Geography, Indian Economy, Environment, GK- Current Affairs, Static General Knowledge
  8. Section 3 | Computer System and Org. (CSO): Basics of COA, Floating Point Rep, Cache Memory Organization, Instr Formats & Modes, Programming the Basic Computer, Input Output Organisation, Register Transfer and Microoperations, Control Unit Design
  9. Section 3 | Database Management System: Basics of DBMS, ER Diagram, Relational Model & Functional Dependencies, Keys & Integrity Constraints, Normalization (1NF - BCNF), Decomposition Properties & 4NF, SQL, File Organization & Indexing, Relational Algebra, Relational Calculus, Transaction Management, Concurrency Control
  10. Section 3 | Operating System: Introduction to OS, Process Management, CPU Scheduling, Threads & Process Creation, Memory Management, Virtual Memory, Disc Scheduling, File Management, Process Synchronization
  11. Section 3 | Computer Networks: Introduction to CN, Data Communication, DLL: Access Control, DLL: Flow Control, DLL: Error Control, Data Link Layer - Ethernet, Net Layer: IPv4 & Proto, Net Layer: IP Addressing, Transport Layer Services, TL: Congestion & UDP, Application Layer, Hardware basics
  12. Section 3 | Data Structures: Introduction to DS, Array, Stack, Queue, Linked List, Tree, Graphs, Hashing, Algorithm Analysis, Time Complexity Analysis, Sorting Algorithms, Greedy Algorithms, Minimum Spanning Trees, Shortest Path Algos
  13. Section 3 | Theory Of Computation & Compiler Design: Introduction to TOC, Deterministic FA (DFA), Non-Deterministic FA, Regular Expressions, Grammar, Regular Language Properties, Moore & Mealy Machines, Pushdown Automata & CFG, Turing Machines, Intro to Compilers, Lexical Analysis, Grammar & CFG, Syntax Analysis: Top-Down, Syntax Analysis: Bottom-Up, Semantic Analysis & SDT, Intermediate Code Gen, Code Optimization
  14. Section 3 | Emerging Trends (AI, Societal Ethics & MS Office): Artificial Intelligence, Emerging Tech Trends, Society, Law & Ethics, MS Office Applications
  15. Section 3 | Software Engineering: Fundamentals of Software Engineering, Software Requirements and Quality Assurance, Software Design, Estimation and Metrics, Software Maintenance and Configuration Management, Software Testing
  16. Section 3 | C Programming: C Fundamentals, Control Flow, Functions, Arrays & Pointers, Storage Classes, Structures & Enums, DMA, Macros, Scoping & File Handling
  17. Section 3 | OOPS, C++, JAVA, HTML: OOPS with C++, Java, HTML Basics, CSS
  18. Section 3 | Java: Java Fundamentals, Array, String, IO & References
  19. Section 3 | Python: Introduction to Python, Tokens, Variables, Data Types, I/O, Operators & Expressions, Control Flow & Looping, Collections & Strings, Functions & Modules, File Handling & Data Analysis
  20. Section 3 | Digital Electronics: Digital Systems & Boolean Basics, Logic Gates & Hardware, Boolean Expression, Boolean Minimization, Combinational Circuit, Sequential Circuits, Number System, Number Representation
  21. Section 3 | Multimedia: Multimedia
  22. BPSC Previous Year Papers:
  23. BPSC Full Mock Tests:
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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