Consider the 5-state DFA 𝑀 accepting the language 𝐿(𝑀) ⊂ (0 + 1)∗ shown…

GATE · 2024 · CS · Set 1 · Computer Science & IT

Consider the 5-state DFA 𝑀 accepting the language 𝐿(𝑀) ⊂ (0 + 1)∗ shown below. For any string 𝑤 ∈ (0 + 1)∗ let $n_0$ (𝑤) be the number of 0 ′ 𝑠 in 𝑤 and $n_1$ (𝑤) be the number of 1′𝑠 in 𝑤.

Which of the following statements is/are FALSE?

A.
States 2 and 4 are distinguishable in 𝑀
B.
States 3 and 4 are distinguishable in 𝑀
C.
States 2 and 5 are distinguishable in 𝑀
D.
Any string 𝑤 with $n_0$ (𝑤) = $n_1$ (𝑤) is in 𝐿(𝑀)

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