NDFA where every string of length =w, <=w, >=w

Duration: 3 min

This video lesson is available to enrolled students.

Return to /learn/COAL-INDIA-MANAGEMENT-TRAINEE/theory-of-computation/non-deterministic-fa/nfa-basics-design/asset-ndfa-where-every-string-of-length-w-w-w after enrolling

Inside: a video lesson and guided study material.

Module outline

  1. About Course: About the Course
  2. Paper-2 | Programming & Data Structures: C Fundamentals, Control Flow, Functions, Arrays & Pointers, Storage Classes, Structures & Enums, DMA, Macros, Scoping & File Handling, Introduction to DS, Array, Stack, Queue, Linked List, Tree, Graphs, Hashing
  3. Paper-2 | Databases / DBMS & SQL: 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
  4. Paper-2 | Algorithms: Algorithm Analysis, Time Complexity Analysis, Sorting Algorithms, Greedy Algorithms, Dynamic Programming, Minimum Spanning Trees, Shortest Path Algos
  5. Paper-2 | Computer Networks & Security: 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 Access Technologies, Network Security
  6. Paper-2 | Digital Logic: Digital Systems & Boolean Basics, Logic Gates & Hardware, Boolean Expression, Boolean Minimization, Combinational Circuit, Sequential Circuits, Number System, Number Representation, Floating Point Rep
  7. Paper-2 | Operating System: Introduction to OS, Process Management, CPU Scheduling, Process Synchronization, Threads & Process Creation, Deadlock, Memory Management, Virtual Memory, Disc Scheduling, File Management
  8. Paper-2 | Theory of Computation: Introduction to TOC, Deterministic FA (DFA), Non-Deterministic FA, Regular Expressions, Grammar, Regular Language Properties, Moore & Mealy Machines, Pushdown Automata & CFG, Turing Machines
  9. Paper-2 | Computer Organization & Architecture: Basics of COA, Cache Memory Organization, Input Output Organisation, Pipelining, Instr Formats & Modes, Control Unit Design, Programming the Basic Computer
  10. Paper-2 | 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. Paper-1 | General Awareness: Polity, Physics, Biology, Chemistry, Static General Knowledge, GK- Current Affairs, History, Geography, Indian Economy, Environment
  12. Paper-1 | Logical Reasoning: Series (Number and Letter Series) (Numerical Relations and Reasoning), Coding Decoding, Non Verbal Reasoning (Spatial Aptitude) (Spatial Reasoning) (Visual Reasoning), Data Interpretation, Blood Relations, Syllogisms, Deductive and Inductive Reasoning (Logical Deduction and Induction) (Prepositional Reasoning), Selection Decision Table (Decision Making), Clock, Calendar, Cubes & Dices, Directions (Direction Test), Analogy, Seating Arrangements, Analytical Reasoning (Counting Figures Reasoning)
  13. Paper-1 | Quantitative Aptitude: Ratio and Proportion (Ratios), Mixture and Alligation, Permutation and Combination, Number System, HCF LCM, Speed Time and Distance, Average, Age Problems, Percentage, Profit and Loss, Time and Work, Pipe and Cistern, Simple Interest and Compound Interest, Powers and Exponents (Surds and Indices), Mensuration and Geometry, Probability, Statistics, Arithmetic, Algebra
  14. Paper-1 | English: Vocabulary, Comprehension / Reading Comprehension / Unseen Passages (Critical Reasoning) (Paragraph Questions), Sentence Re-arrangements (Para Jumbles) (Narrative Sequencing), Sentence Correction (Error Correction), Sentence Completion (Fill in the blanks), Sentence Construction, Cloze Test (Cloze Passage)
  15. Coal India Previous Year Paper:
  16. Engineering Mathematics: Set Theory, Relations, Functions, Graph Theory, Group Theory, Propositional and Predicate Logic, Linear Algebra, Calculus
  17. Coal India Mock Test:
AI summary & chapters

AI Summary

An AI-generated summary of this video lecture.

The video lecture focuses on designing Nondeterministic Finite Automata (NFA) for specific string length constraints over the binary alphabet $\Sigma = \{a, b\}$. The instructor systematically addresses three distinct conditions: strings of length exactly 3, strings of length less than or equal to 3, and strings of length greater than or equal to 3. Through step-by-step board work, he demonstrates how to construct state transitions and define final states to satisfy these length requirements, providing a clear visual guide for students learning formal language theory and automata construction techniques.

Chapters

  1. 0:00 – 2:00 00:00-02:00

    The instructor begins by presenting the problem statement on the whiteboard: "Design a NFA that accepts all strings over the alphabet $\Sigma = \{a, b\}$, such that every string 'w' accepted must be like i) $|w| = 3$". He starts constructing the automaton by drawing the initial state $q_0$. He then draws a transition arrow to a new state $q_1$, labeling it with "$a, b$" to indicate that either character can be read. He repeats this process, drawing transitions from $q_1$ to $q_2$ and then from $q_2$ to $q_3$, all labeled with "$a, b$". Finally, he encircles $q_3$ with a double line to designate it as the accepting state, ensuring the machine stops accepting after exactly three characters.

  2. 2:00 – 3:29 02:00-03:29

    Next, the instructor tackles condition ii) $|w| <= 3$. He draws a new linear chain of states $q_0, q_1, q_2, q_3$ with transitions labeled "$a, b$". To satisfy the "less than or equal" condition, he marks every single state in the chain ($q_0, q_1, q_2, q_3$) as a final state using double circles. This allows the machine to accept the empty string, single characters, two-character strings, or three-character strings. He then moves to condition iii) $|w| >= 3$. He draws a similar chain ending at $q_3$, marking $q_3$ as final. Crucially, he adds a self-loop on $q_3$ labeled "$a, b$", allowing the machine to consume any number of additional characters after the third one, thus accepting strings of length 3 or greater.

The lecture demonstrates a fundamental pattern in automata design where the structure of the state diagram dictates the length of accepted strings. By manipulating which states are designated as final and adding self-loops, the instructor shows how to create NFAs for exact, upper-bounded, and lower-bounded length constraints. This progression highlights the flexibility of NFAs in handling simple numerical properties of string length without complex logic, serving as a foundational example for understanding regular languages and the power of state transitions in formal computation and theoretical computer science.

Loading lesson…