Practice Problem on First Function
Duration: 8 min
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Inside: a video lesson and guided study material.
Module outline
- Discrete Mathematics: Permutation, Combination and Probability / क्रमचय, संचय एवं प्रायिकता, Set Theory, Relations, Functions, Propositional and Predicate Logic, Graph Theory, Group Theory
- Digital Logic: Digital Systems & Boolean Basics, Boolean Expression, Boolean Minimization, Logic Gates & Hardware, Combinational Circuit, Sequential Circuits, Number System, Number Representation, Floating Point Rep
- Computer Organization and Architecture: Basics of COA, Programming the Basic Computer, Cache Memory Organization, Input Output Organisation, Instr Formats & Modes, Register Transfer and Microoperations, Control Unit Design, Pipelining, Multiprocessors
- Programming: Language Design, C Fundamentals, Control Flow, Functions, Arrays & Pointers, Storage Classes, Structures & Enums, DMA, Macros, Scoping & File Handling, OOPS with C++
- Data Structures: Introduction to DS, Array, Linked List, Stack, Queue, Tree, Graphs, Hashing
- Algorithms: Algorithm Analysis, Time Complexity Analysis, Sorting Algorithms, Greedy Algorithms, Dynamic Programming, Minimum Spanning Trees, Shortest Path Algos, Advanced Algorithms
- Theory of Computation: Grammar, Regular Language Properties, Moore & Mealy Machines, Turing Machines
- Compiler Design: 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, Introduction to TOC, Deterministic FA (DFA), Non-Deterministic FA, Regular Expressions, Pushdown Automata & CFG, Complexity Theory
- Operating Systems: Introduction to OS, Process Management, CPU Scheduling, Process Synchronization, Threads & Process Creation, Deadlock, Memory Management, Virtual Memory, Disc Scheduling, File Management, Unix OS, Linux OS, Security
- Database Management Systems: Basics of DBMS, ER Diagram, Relational Model & Functional Dependencies, Keys & Integrity Constraints, Normalization (1NF - BCNF), Decomposition Properties & 4NF, File Organization & Indexing, Relational Algebra, SQL, Relational Calculus, Transaction Management, Concurrency Control, ORDBMS, NoSQL
- Computer Networks: 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
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
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.
2:00 – 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.
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.