GATE 1989 Subject – Theory Of Computation Topic -Finite Automata
GATE 1989 Subject – Theory Of Computation Topic -Finite Automata
Here’s a focused breakdown of the GATE 1989 paper, particularly for the Theory of Computation subject under the topic Finite Automata:
Contents [hide]
- 1
GATE 1989 – Theory of Computation
- 1.1
Topic: Finite Automata
- 1.2
Key Concepts to Revise
- 1.3
Sample GATE 1989 Style Question (Finite Automata)
- 1.4
Conceptual Question Example
- 1.5
Useful Tips for Finite Automata Questions in GATE
- 1.6
Recommended Practice Problems
- 1.7
GATE 1989 – Theory of Computation
- 1.8 GATE 1989 Subject – Theory Of Computation Topic -Finite Automata
- 1.1
GATE 1989 – Theory of Computation
Topic: Finite Automata
Key Concepts to Revise
Before jumping into specific questions or examples from the 1989 paper, it’s important to revise the following key concepts related to Finite Automata:
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Deterministic Finite Automata (DFA)
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Non-Deterministic Finite Automata (NFA)
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Equivalence of DFA and NFA
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Conversion: NFA to DFA
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Minimization of DFA
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Regular Languages and Regular Expressions
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Language accepted by FA
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Closure Properties of Regular Languages
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Limitations of FA (e.g., not recognizing context-free languages)
Sample GATE 1989 Style Question (Finite Automata)
Q1.
Which of the following statements is true?
a) Every NFA is also a DFA
b) Every DFA is also an NFA
c) Every regular language is not accepted by DFA
d) NFA can recognize non-regular languages
Correct Answer: (b)
Every DFA is also an NFA (a special case of NFA with exactly one transition per symbol per state).
Option (a) is false because not all NFAs are DFAs without conversion.
Option (c) is false because every regular language is accepted by a DFA.
Option (d) is false because NFAs cannot recognize non-regular languages.
Conceptual Question Example
Q2.
Let L be a language accepted by a DFA. Which of the following statements is true?
a) L is necessarily infinite
b) Complement of L is not regular
c) L is regular
d) L cannot be described by a regular expression
Correct Answer: (c)
Any language accepted by a DFA is by definition a regular language.
Useful Tips for Finite Automata Questions in GATE
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Always draw a state diagram to better visualize transitions.
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Practice converting regular expressions to FA and vice versa.
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Be familiar with DFA minimization techniques (state equivalence method).
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Remember that every DFA is a unique NFA, but the reverse requires construction.
Recommended Practice Problems
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Construct a DFA that accepts strings over
{0,1}
that end with01
. -
Convert the given NFA to DFA.
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Minimize a given DFA and find its language.
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Given a regular expression, construct the equivalent NFA and DFA.
Would you like the exact GATE 1989 question paper with solutions, or should I generate a custom practice test based on that year’s style and syllabus?
Certainly! Let’s delve into a specific question from the GATE 1989 examination under the subject Theory of Computation, focusing on the topic of Finite Automata.
GATE 1989 – Theory of Computation
Topic: Finite Automata
Question:
Is the class of regular sets closed under infinite union? Explain.
Answer:
The class of regular languages is not closed under infinite union.
Explanation:
Regular languages are closed under operations such as union, intersection, and complement when applied finitely. However, when considering an infinite union of regular languages, the resulting language may not be regular.
Example:
Consider the set of languages:
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L₁ = { a }
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L₂ = { aa }
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L₃ = { aaa }
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…
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Lₙ = { aⁿ }
Each Lₙ is regular. Now, consider the infinite union:
L = ⋃ₙ₌₁^∞ Lₙ = { a, aa, aaa, aaaa, … } = { aⁿ | n ≥ 1 }
This language is regular and can be represented by the regular expression a⁺.
However, consider a different example:
Let Lₙ = { aⁿbⁿ } for each n ≥ 1. Each Lₙ is finite and thus regular. Now, consider the union:
L = ⋃ₙ₌₁^∞ Lₙ = { ab, aabb, aaabbb, … } = { aⁿbⁿ | n ≥ 1 }
This language is not regular, as it requires matching numbers of a’s and b’s, which cannot be done with a finite automaton.
Therefore, the infinite union of regular languages is not necessarily regular, indicating that the class of regular languages is not closed under infinite union.
If you’re interested in exploring more questions from GATE 1989 or other years, or if you need further clarification on topics within the Theory of Computation, feel free to ask!