DFA Designing where string ends with substring ‘s’

Duration: 12 min

This video lesson is available to enrolled students.

Return to /learn/BPSC/part-3-theory-of-computation/deterministic-fa-dfa/dfa-construction-design/asset-dfa-designing-where-string-ends-with-substring-s after enrolling

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.

The video is an educational lecture on automata theory, specifically focusing on the design of minimal Deterministic Finite Automata (DFA). The instructor, Sanchit Jain, presents a problem: construct a minimal DFA that accepts all strings over the alphabet {a, b} where every accepted string 'w' ends with a specific substring 's'. He outlines three distinct examples to solve: i) s = ab, ii) s = aa, and iii) s = bab. The lecture proceeds by solving these examples sequentially, drawing the state diagrams on a digital whiteboard. The instructor begins by defining the language for the first example, then constructs the DFA state by state, adding self-loops and back-transitions to handle overlapping patterns. He concludes with a general formula for the number of states required based on the length of the substring.

Chapters

  1. 0:00 – 2:00 00:00-02:00

    The video begins with a lecture on automata theory, specifically focusing on the design of minimal Deterministic Finite Automata (DFA). The problem statement is displayed on the screen: 'Q design a minimal DFA that accepts all strings over the alphabet {a, b}, where every accepted string 'w' ends with substring 's'.' The instructor lists three specific cases to solve: i) s = ab, ii) s = aa, and iii) s = bab. He starts by analyzing the first case, s = ab. He writes the language set L = {ab, aab, bab, bbaab, ...} to illustrate the types of strings that should be accepted. He begins constructing the DFA by drawing the initial state q0. He draws a transition labeled 'a' leading to a new state q1, and then a transition labeled 'b' from q1 to a final state q2. This establishes the basic path for the substring 'ab'. The instructor's name, SANCHIT JAIN, and the logo KNOWLEDGEGATE are visible on the screen.

  2. 2:00 – 5:00 02:00-05:00

    The instructor refines the DFA for s = ab by adding necessary loops and back-transitions. He adds a self-loop on q0 labeled 'b' to handle strings starting with 'b' (like 'bab'). He adds a self-loop on q1 labeled 'a' to handle strings like 'aab'. Crucially, he addresses transitions from the final state q2. He draws a transition from q2 labeled 'a' back to q1, explaining that if the string is 'aba', it ends in 'a', which is the prefix of 'ab'. He draws a transition from q2 labeled 'b' back to q0, as 'abb' ends in 'bb' and has no prefix of 'ab'. This completes the minimal DFA for the first example. He writes examples like 'bbab' and 'bab' on the board to verify the logic. The diagram shows q0 with a loop on 'b', an arrow to q1 on 'a', q1 with a loop on 'a', an arrow to q2 on 'b', and transitions from q2 back to q0 and q1.

  3. 5:00 – 10:00 05:00-10:00

    The lecture moves to the third example, s = bab. The instructor draws a new DFA with four states: q0, q1, q2, and q3. The path is q0 ->(b) q1 ->(a) q2 ->(b) q3, where q3 is the final state. He explains the transitions for overlapping patterns. For instance, if the machine is in q2 (having seen 'ba') and receives an 'a', it goes to q1 because 'baa' ends in 'a', the first character of 'bab'. If in q3 (having seen 'bab') and receives an 'a', it goes to q1 because 'baba' ends in 'a'. He also draws transitions for 'b' inputs from the final state, ensuring the machine resets or moves to the correct prefix state. He writes examples like 'bbab' and 'babab' on the board to verify the transitions. He also draws a self-loop on q0 for 'a' to handle strings starting with 'a'. The diagram shows curved arrows indicating back-transitions from the final state to earlier states.

  4. 10:00 – 12:18 10:00-12:18

    The video concludes with a summary slide titled 'Conclusion'. The instructor writes a general rule: 'if w = xs, |s| = m, then no of states in the DFA is m+1'. He underlines 'no need of dead state' and notes that the machine 'can not stay of final state for ever' (implying the final state is not a sink state unless the pattern is trivial). This provides a quick formula for students to determine the number of states required for any substring 's' without drawing the full automaton. He emphasizes that the number of states is simply the length of the substring plus one. The slide text is clearly visible and serves as a takeaway for the lecture.

The video provides a comprehensive guide to constructing minimal DFAs for suffix patterns. It moves from specific examples to a general rule, emphasizing the logic of state transitions and prefix matching. The instructor demonstrates how to handle overlapping patterns and self-loops, ensuring the DFA correctly identifies strings ending with the target substring. The final conclusion offers a concise formula for determining the number of states, simplifying the design process for students.

Loading lesson…