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Questions and Answers
Any NFA having n states can be converted to a DFA having at most (select the smallest possible value)
Any NFA having n states can be converted to a DFA having at most (select the smallest possible value)
- 2n states (correct)
- n2 states
- 3n states
- 2n states (correct)
What is the minimum number of states required for a DFA that accepts the language L = {w | the number of 1’s in w is divisible by 3}?
What is the minimum number of states required for a DFA that accepts the language L = {w | the number of 1’s in w is divisible by 3}?
- 1
- 4
- 2
- 3 (correct)
What is the ϵ-closure of state q1 in the given NFA?
What is the ϵ-closure of state q1 in the given NFA?
- {q0, q1} (correct)
- {q1}
- {q0, q1, q2, q3}
- {q0, q1, q2}
Which of the following strings is accepted by the DFA below?
Which of the following strings is accepted by the DFA below?
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Let L1 and L2 be two regular languages. What can we say about the language L = {w1 w2 | w1 ∈ L1, w2 ∈ L2}?
Let L1 and L2 be two regular languages. What can we say about the language L = {w1 w2 | w1 ∈ L1, w2 ∈ L2}?
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What is the language accepted by the given NFA?
What is the language accepted by the given NFA?
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Study Notes
NFA to DFA Conversion
- An NFA with n states can be converted to a DFA with at most 2^n states, since the states of the DFA correspond to subsets of the NFA's states.
Counting States in DFA
- For the language L = {w | the number of 1’s in w is divisible by 3}, a DFA requires a minimum of 3 states to track the count of 1's modulo 3.
ε-Closure in NFA
- The ε-closure of a state q includes all states reachable from q through ε-transitions only. For state q1, the ε-closure is {q0, q1}.
Accepted Strings by DFA
- The DFA accepts the string "01011101". Other provided strings do not lead to the accept state.
Regular Languages Concatenation
- The concatenation of two regular languages L1 and L2 results in a language L that is guaranteed to also be regular.
NFA Accepted Language
- The language accepted by a specific NFA includes strings that either begin with 0 or end with 1. Verification involves checking for computation paths leading to accept states based on input string characteristics.
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