GATE 1994 Theory Of Computation Topic -Finite Automataj9

GATE 1994 Theory Of Computation Topic -Finite Automata

The GATE 1994 exam included Theory of Computation, and one of the fundamental topics in this domain is Finite Automata. Let’s go through the key concepts related to Finite Automata (FA) that might be relevant to GATE questions.

 What is Finite Automata (FA)?

A Finite Automaton is a mathematical model of a computation system that consists of:

• A finite set of states
• A finite input alphabet
• A transition function
• A start state
• A set of accepting (final) states

Types of Finite Automata

There are two main types of Finite Automata:

1. Deterministic Finite Automaton (DFA)

   • For each state and input symbol, there is exactly one transition.
   • Example: A DFA recognizing binary strings that end with 01.

2. Non-Deterministic Finite Automaton (NFA)

   • For a given state and input symbol, there can be multiple transitions.
   • Can have ε (epsilon) transitions (moves without consuming input).
   • Example: An NFA recognizing binary strings containing 11 anywhere in the string.

 Formal Definition of DFA

A DFA is a 5-tuple:

(Q,Σ,δ,q0,F)(Q, \Sigma, \delta, q_0, F)(Q,Σ,δ,q0​,F)

where:

• Q → Finite set of states
• Σ → Finite input alphabet
• δ → Transition function (δ: Q × Σ → Q)
• q₀ → Initial state (q₀ ∈ Q)
• F → Set of final (accepting) states (F ⊆ Q)

Example DFA

Let’s define a DFA that accepts binary strings ending with ’01’.

States:

• q0 (Start State)
• q1 (Reads ‘0’)
• q2 (Reads ’01’ – Final State)

 NFA vs DFA

Key Fact: Every NFA can be converted into an equivalent DFA (using the subset construction method).

 Applications of Finite Automata

Lexical Analysis in Compilers
Pattern Matching (Regular Expressions, String Searching)
Protocol Design in Networking
Text Processing (e.g., Searching for keywords in a document)

 GATE 1994 Sample Question (Finite Automata)

Question:
Which of the following statements is true?
A) Every NFA has an equivalent DFA.
B) DFA is more powerful than NFA.
C) NFA can recognize more languages than DFA.
D) Some regular languages cannot be recognized by DFA.

Answer:  (A) Every NFA has an equivalent DFA.
Explanation: DFA and NFA recognize the same class of languages (Regular Languages), but DFA has unique transitions while NFA allows multiple transitions.

Would you like more GATE-style practice questions or explanations on converting NFA to DFA?

In the GATE 1994 Computer Science exam, a notable question in the Theory of Computation section focused on Finite Automata. This question required candidates to determine the regular expression corresponding to a given finite state automaton.(ExamSIDE)

GATE 1994 Finite Automata Question Overview

• Topic: Finite Automata & Regular Expressions
• Question Type: Subjective
• Marks: 2
• Task: Derive the regular expression for the language recognized by the provided finite state automaton.(ExamSIDE, ExamSIDE, Gate Overflow)

While the specific diagram of the automaton isn’t provided here, the question tested the ability to analyze state transitions and construct the equivalent regular expression that defines the same language.

Solution Approach

To solve such a problem, one typically follows these steps:

1. Understand the Automaton: Analyze the states, transitions, start state, and accepting states of the given finite automaton.
2. Identify Patterns: Look for loops, paths, and sequences that lead to accepting states.
3. Construct Regular Expressions for Paths: For each path from the start state to an accepting state, construct a regular expression that represents the sequence of inputs along that path.
4. Combine Expressions: Use union ( + ), concatenation, and Kleene star ( * ) operations to combine the expressions for different paths into a single regular expression that represents the entire language accepted by the automaton.(Wikipedia)

This method ensures that all accepted strings are captured by the resulting regular expression.(ExamSIDE)

Video Explanation

For a visual and detailed explanation of this and similar problems, you can refer to the following video:

Regular Expressions – ALL GATE PYQs – Part 1 | Finite Automata

This video covers various GATE questions related to regular expressions and finite automata, providing step-by-step solutions and insights.

If you need further clarification or assistance with specific aspects of finite automata or regular expressions, feel free to ask!

GATE 1994 Theory Of Computation Topic -Finite Automataj9