Practice Question - 3

Duration: 4 min

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Inside: a video lesson and guided study material.

Module outline

  1. HPSC Interview Preparation: Interview Preparation
  2. Python Language: Introduction to Python, Tokens, Variables, Data Types, I/O, Operators & Expressions, Control Flow & Looping, Collections & Strings, Functions & Modules, File Handling & Data Analysis, DSA using Python
  3. Data Structure & Algorithms: Introduction to DS, Array, Stack, Queue, Linked List, Tree, Graphs, Hashing, Algorithm Analysis, Sorting Algorithms, Minimum Spanning Trees, Time Complexity Analysis, Graph Theory, Shortest Path Algos
  4. Computer Networks: Introduction to CN, Data Communication, DLL: Access Control, DLL: Flow Control, Data Link Layer - Ethernet, Net Layer: IPv4 & Proto, Net Layer: IP Addressing, Transport Layer Services, TL: Congestion & UDP, Application Layer, Hardware basics, Network Security
  5. Computer System & Organisation: Basics of COA, Cache Memory Organization, Input Output Organisation, Pipelining, Instr Formats & Modes, Control Unit Design, Programming the Basic Computer
  6. 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, Transaction Management, Concurrency Control
  7. Operating Systems: Introduction to OS, Process Management, CPU Scheduling, Process Synchronization, Deadlock, Threads & Process Creation, Memory Management, Virtual Memory, Disc Scheduling
  8. Digital Logic & Circuits: Digital Systems & Boolean Basics, Logic Gates & Hardware, Boolean Expression, Boolean Minimization, Combinational Circuit, Sequential Circuits, Number System, Number Representation
  9. Theory Of Computation: Introduction to TOC, Deterministic FA (DFA), Non-Deterministic FA, Regular Expressions, Grammar, Regular Language Properties, Pushdown Automata & CFG, Turing Machines, Moore & Mealy Machines
  10. 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
  11. Software Engineering: Fundamentals of Software Engineering, Software Requirements and Quality Assurance, Software Design, Estimation and Metrics, Software Testing, Software Maintenance and Configuration Management, Data Warehousing & Mining
  12. Introduction to Emerging Trends: Emerging Tech Trends, समुच्चय, संबंध, फलन और विविक्त गणित / Sets, Relations, Functions and Discrete Mathematics, व्यापार, विपणन एवं उपभोक्ता संरक्षण / Trade, Marketing and Consumer Protection, कंप्यूटर नेटवर्क / Computer Networks
  13. Digital Society & Cyber Law: Society, Law & Ethics, साइबर सुरक्षा / Cyber Safety and Security
  14. HPSC PGT Previous Year Paper:
  15. HPSC Assistant Professor Previous Year Paper:
  16. Live Sessions: HPSC Live Sessions, EMRS TGT/PGT Live Class
  17. Full Mock Test:
  18. HPSC PGT - MOCK Test Series:
AI summary & chapters

AI Summary

An AI-generated summary of this video lecture.

The video lecture presents a step-by-step construction of a Pushdown Automaton (PDA) for the language $L = \{ww^r \mid w \in \{a, b\}^*\}$. The instructor defines the language as a string $w$ concatenated with its reverse $w^r$. He illustrates this with the example $w = aaba$, resulting in $aabaabaa$. The lecture focuses on drawing the PDA state diagram, starting with an initial state $q_0$ that pushes input symbols onto the stack. He introduces a non-deterministic transition to state $q_1$ to guess the midpoint and match the reverse string by popping symbols. The session concludes with a theoretical overview of Non-Deterministic PDAs (NPDA), defining them using 7 tuples and explaining the transition function that allows movement to multiple states.

Chapters

  1. 0:00 – 2:00 00:00-02:00

    The instructor introduces the problem statement: "Construct pda that accepts a language $L = \{ww^r \mid w \in \{a, b\}^*\}$". He explains the language structure where a string $w$ is followed by its reverse $w^r$. He provides an example: $w = aaba$ and $w^r = abaa$, forming $aabaabaa$. He begins the PDA construction by drawing the initial state $q_0$ with a self-loop. He writes transition rules like $a, a / aa$, $a, b / ab$, $b, a / ba$, and $b, b / bb$. These transitions show the PDA pushing input symbols onto the stack to store $w$. He also draws a transition from $q_0$ to state $q_1$ labeled $a, a / \epsilon$ and $b, b / \epsilon$, representing the non-deterministic choice to start matching the reverse string.

  2. 2:00 – 4:08 02:00-04:08

    The instructor refines the PDA diagram, circling the transition from $q_0$ to $q_1$ to highlight the non-deterministic guess of the string's midpoint. He explains that in state $q_1$, the PDA matches input against the stack. He draws a self-loop on $q_1$ with transitions $a, a / \epsilon$ and $b, b / \epsilon$, popping the stack if inputs match. A transition to final state $q_2$ with $\epsilon, Z / Z$ indicates acceptance. The video then shifts to a slide titled "Non-Deterministic PDA". It defines an NPDA using 7 tuples and highlights the transition function $\delta: Q imes (\Sigma \cup \{\epsilon\}) imes \Gamma o 2^{Q imes \Gamma^*}$. The instructor explains that an NPDA can move to multiple states for a given input and stack symbol, essential for languages like palindromes where the midpoint is unknown. He notes that the rest of the tuples remain the same as a DPDA.

The lecture bridges practical construction and theoretical definition. It demonstrates how non-determinism allows PDAs to handle unknown midpoints in palindromes by pushing the first half and non-deterministically switching to pop and match the second half. The session concludes by formalizing this concept through the mathematical definition of an NPDA.

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