Practice Questions DFA

Duration: 2 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
  13. Digital Society & Cyber Law: Society, Law & Ethics
  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 focuses on determining the minimum number of states required for Finite Automata to recognize specific languages based on counting properties. The instructor presents a problem involving a binary alphabet $\Sigma = \{0, 1\}$ and asks for the number of states needed to accept words with an odd number of 1s. He then transitions to a second problem concerning the length of strings divisible by a specific number, illustrating the general rule for constructing minimal automata for modular arithmetic conditions.

Chapters

  1. 0:00 – 1:42 00:00-01:42

    The instructor starts by displaying a multiple-choice question on the screen: 'Let $\Sigma = \{0, 1\}$, then an automaton A accepting only those words from $\Sigma$ having an odd number of 1's requires _______ states including the start state'. The options provided are 2, 3, 4, and 5. He analyzes the condition mathematically, writing $|w|_1 = 1 \pmod 2$ on the whiteboard to represent the requirement that the count of 1s must be odd. He explains that modulo 2 arithmetic implies two distinct equivalence classes: even and odd. Consequently, he deduces that the automaton requires exactly 2 states—one to track the even count (start state) and one to track the odd count (accepting state). He underlines option (a) 2. Next, he introduces a second question: 'The smallest finite automaton which accepts the language $\{x \mid ext{length of } x ext{ is divisible by } 500\}$ has _______ states'. The options are 200, 300, 400, and 500. He writes the condition $|w| = 0 \pmod{500}$ to formalize the divisibility rule. He explains the general principle that for a language requiring the length of the string to be divisible by $n$, the minimal automaton requires $n$ states to count the length modulo $n$. He emphasizes that the number of states equals the modulus. Therefore, for divisibility by 500, he concludes that 500 states are necessary. He underlines option (d) 500 as the correct answer.

The lesson demonstrates a fundamental property of Finite Automata: the number of states required corresponds to the number of distinct remainders needed to track a specific property. For counting parity (odd/even), 2 states suffice. For counting length modulo $n$, $n$ states are required. This establishes a direct relationship between the modulus of the condition and the state complexity of the automaton.

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