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Sumit

The document presents a presentation by Sumit Prasad on constructing a Deterministic Finite Automata (DFA) that accepts all binary strings except '000' and '111'. It outlines the basic concepts of DFA, the state diagram, transition table, and provides examples of accepted and rejected strings. The conclusion emphasizes the successful design of the DFA and mentions real-world applications such as lexical analysis and pattern matching.

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9 views16 pages

Sumit

The document presents a presentation by Sumit Prasad on constructing a Deterministic Finite Automata (DFA) that accepts all binary strings except '000' and '111'. It outlines the basic concepts of DFA, the state diagram, transition table, and provides examples of accepted and rejected strings. The conclusion emphasizes the successful design of the DFA and mentions real-world applications such as lexical analysis and pattern matching.

Uploaded by

subhajit12225
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
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Download as PDF, TXT or read online on Scribd
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CA 1 PRESENTATION

●
NAME:Sumit Prasad
●
ROLL NO:10200223053
●
SUBJECT:FORMAL LANGUAGE AND & AUTOMATA
THOERY
●
SUBJECT CODE:PCC-CS403
●
TOPIC:CONSTRUCT A DFA THAT ACCEPTS ALL
BINARY STRINGS EXCEPT ‘000’ AND ‘111’.
●
BRANCH:IT
●
SEM:4TH

1
Introduction
• Deterministic Finite Automata (DFA) is a
theoretical machine used to recognize patterns in
strings.

2
Problem Statement

• Construct a DFA that accepts all binary strings


except '000' and '111'.

3
Basic Concepts of DFA

• A DFA consists of:


• - A finite set of states
• - An alphabet (Σ={0,1})
• - A transition function
• - An initial state
• - A set of accepting states

4
Understanding the Exclusions

• The DFA must reject '000' and '111', meaning it


should track the last three bits of the string.

5
State Diagram Concept
• A state diagram represents how the DFA
transitions between states based on inputs.

6
State Representation
• Each state should store the last three bits
processed to detect '000' and '111'.

7
Transition Table

• A transition table helps


in defining how the
DFA moves from one
state to another based
on input symbols.

8
State Diagram

• The DFA will have


transitions that ensure
it rejects '000' and
'111' while accepting
all other strings.

9
Explanation of Transitions
• Each transition ensures the last three bits are
checked, moving to accepting or rejecting states.

10
Testing with Examples
• Example 1: 101 (Accepted)
• Example 2: 000 (Rejected)
• Example 3: 1101 (Accepted)

11
Minimization of DFA
• The DFA can be optimized by merging equivalent
states to reduce complexity.

12
Real-world Applications
• DFAs are used in:
• - Lexical analysis in compilers
• - Pattern matching
• - Network protocol design

13
Conclusion
• We successfully designed a DFA that accepts all
binary strings except '000' and '111'.

14
References & Acknowledgment

• 1. Hopcroft, Ullman - Automata Theory


• 2. Lecture Notes on DFAs
• 3. Online DFA Simulators

15
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