DFA Designing where starts with s = aaa or bbb

Duration: 6 min

This video lesson is available to enrolled students.

Return to /learn/IBPS-SO-IT-PRELIMS/theory-of-computation/deterministic-fa-dfa/dfa-construction-design/asset-dfa-designing-where-starts-with-s-aaa-or-bbb after enrolling

Inside: a video lesson and guided study material.

Module outline

  1. About Course: About the Course
  2. English Language: Vocabulary, Noun, Adjectives, Tenses, Pronoun, Adverb, Preposition, Conjunction, Active Passive Voice (Voice), Articles, Direct and Indirect Speech, Sentence Correction (Error Correction), Sentence Re-arrangements (Para Jumbles) (Narrative Sequencing), Comprehension / Reading Comprehension / Unseen Passages (Critical Reasoning) (Paragraph Questions), Sentence Completion (Fill in the blanks), Cloze Test (Cloze Passage)
  3. Reasoning: Series (Number and Letter Series) (Numerical Relations and Reasoning), Coding Decoding, Data Sufficiency, Puzzle Solving (Puzzles), Seating Arrangements, Blood Relations, Syllogisms, Inequality, Directions (Direction Test), Deductive and Inductive Reasoning (Logical Deduction and Induction) (Prepositional Reasoning), Clock, Calendar, Analytical Reasoning (Counting Figures Reasoning), Selection Decision Table (Decision Making), Cubes & Dices, Machine Input-Output
  4. Quantitative Aptitude: Ratio and Proportion (Ratios), Data Interpretation, Mixture and Alligation, Permutation and Combination, Number System, Sequence and Series (Series), Speed Time and Distance, Algebra, Speed Mathematics and Basic Mathematics, Percentage, Average, Time and Work, Simple Interest and Compound Interest, Profit and Loss, Age Problems, Partnership, Mensuration and Geometry, Probability, IBPS Specific Videos
  5. Data Structures - Professional Knowledge: Introduction to DS, Array, Stack, Queue, Linked List, Tree, Graphs, Hashing
  6. Algorithms- Professional Knowledge: Algorithm Analysis, Time Complexity Analysis, Sorting Algorithms, Greedy Algorithms, Dynamic Programming, Minimum Spanning Trees, Shortest Path Algos
  7. Python- Professional Knowledge: Python for Placements by Yash Sir, Python Basics
  8. Operating System- Professional Knowledge: Introduction to OS, Process Management, CPU Scheduling, Deadlock, Threads & Process Creation, Memory Management, Virtual Memory, Disc Scheduling, File Management
  9. DBMS + SQL- Professional Knowledge: Basics of DBMS, ER Diagram, Relational Model & Functional Dependencies, Keys & Integrity Constraints, Normalization (1NF - BCNF), File Organization & Indexing, SQL, Transaction Management, Concurrency Control
  10. Computer Networks- Professional Knowledge: Introduction to CN, Data Communication, Net Layer: IP Addressing, Net Layer: IPv4 & Proto, Application Layer, Hardware basics, Network Security
  11. Software Engineering- Professional Knowledge: Fundamentals of Software Engineering, Software Requirements and Quality Assurance, Software Design, Estimation and Metrics, Software Testing, Software Maintenance and Configuration Management
  12. Computer Organization & Microprocessor- Professional Knowledge: Basics of COA, Cache Memory Organization, Programming the Basic Computer
  13. Digital Logic Design- Professional Knowledge: Digital Systems & Boolean Basics, Logic Gates & Hardware, Boolean Expression, Boolean Minimization, Combinational Circuit, Sequential Circuits, Number System, Number Representation
  14. Theory of Computation- Professional Knowledge: Introduction to TOC, Deterministic FA (DFA), Non-Deterministic FA, Regular Expressions, Regular Language Properties, Pushdown Automata & CFG, Turing Machines
  15. Compiler Design- Professional Knowledge: Intro to Compilers, Lexical Analysis, Grammar & CFG, Syntax Analysis: Top-Down, Intermediate Code Gen, Code Optimization
  16. Programming Languages- Professional Knowledge: C Programming by Yash Sir, Object Oriented Programming (OOPS), Programming in C++, Java, C Language Core
  17. Emerging Tech- Professional Knowledge: Emerging Tech Trends
  18. Artificial Intelligence: Artificial Intelligence
  19. Unit Test - Professional Knowledge:
  20. Full Length Mock Test:
AI summary & chapters

AI Summary

An AI-generated summary of this video lecture.

The video lecture focuses on designing minimal Deterministic Finite Automata (DFAs) for specific language constraints. The problem asks for a DFA that accepts strings $w$ where $w = sX$, meaning the string must start with a specific prefix $s$ followed by any string $X$. The instructor tackles two cases: $s = aa/bb$ and $s = aaa/bbb$. He systematically constructs the state diagrams, defining start states, transitions for valid prefixes, accepting states, and dead states for invalid prefixes. The lecture emphasizes the importance of handling all possible input combinations to ensure the DFA is complete and minimal.

Chapters

  1. 0:00 – 2:00 00:00-02:00

    The instructor introduces the problem statement on the whiteboard: 'Design a minimal DFA that accepts all strings over the alphabet $\Sigma = \{a, b\}$ such that every accepted string $w$, is like $w=sX$.' He begins with case (i) where $s = aa/bb$. He draws the initial state $q_0$ and branches into two paths: one for 'a' leading to $q_1$ and one for 'b' leading to $q_3$. He continues the 'a' path to $q_2$ (accepting) and the 'b' path to $q_4$ (accepting). He adds self-loops on the accepting states $q_2$ and $q_4$ for inputs 'a' and 'b' to satisfy the $X$ part of $w=sX$. He also introduces a dead state $q_5$ for invalid transitions like 'ab' or 'ba' after the first character. He explicitly draws the transition from $q_1$ on 'b' to $q_5$ and from $q_3$ on 'a' to $q_5$. He ensures $q_5$ has self-loops for 'a' and 'b'.

  2. 2:00 – 5:00 02:00-05:00

    The instructor moves to case (ii) where $s = aaa/bbb$. He starts a new diagram with state $q_0$. He draws a path for 'a': $q_0 \xrightarrow{a} q_1 \xrightarrow{a} q_2 \xrightarrow{a} q_3$. He draws a parallel path for 'b': $q_0 \xrightarrow{b} q_4 \xrightarrow{b} q_5 \xrightarrow{b} q_3$. He marks $q_3$ as the single accepting state for both paths. He adds self-loops on $q_3$ for 'a' and 'b'. He then defines a dead state $q_6$ to handle any deviation from the required prefixes (e.g., 'ab' or 'ba' sequences). Transitions from intermediate states ($q_1, q_2, q_4, q_5$) on the wrong input character lead to $q_6$. For instance, from $q_1$ on 'b' goes to $q_6$, and from $q_2$ on 'b' goes to $q_6$. Similarly for the 'b' path, transitions on 'a' lead to $q_6$.

  3. 5:00 – 6:16 05:00-06:16

    The instructor finalizes the DFA for case (ii). He points to the dead state $q_6$ and explains that it has self-loops for both 'a' and 'b', ensuring that once an invalid prefix is detected, the string is rejected. He reviews the entire diagram, highlighting how the structure ensures that only strings starting with 'aaa' or 'bbb' reach the accepting state $q_3$. He concludes the explanation of the minimal DFA construction for this specific language constraint. He emphasizes that the state $q_3$ acts as a sink for all valid strings that have met the prefix requirement.

The lecture effectively demonstrates the construction of DFAs for prefix-based languages. By breaking down the problem into valid prefix paths and invalid transition paths (dead states), the instructor shows how to ensure minimality and correctness. The transition from a simple 2-character prefix to a 3-character prefix illustrates the scalability of the DFA design method. The use of a common accepting state for both 'a' and 'b' paths in the second case highlights optimization techniques in DFA design.

Loading lesson…