Consider the 5-state DFA $M$ accepting the language $L(M)=(0+1)^*$. For any string $w\in(0+1)^*$, let $n_0(w)$ be the number of 0s in $w$ and $n_1(w)$ be the number of 1s in $w$. Which of the following statements is/are FALSE?

Question

Accepted Answer

Any string $w$ with $n_0(w)=n_1(w)$ is in $L(M)$. The language $(0+1)^*$ is the set of all strings over the alphabet $\{0,1\}$, so every binary string belongs to it. Therefore the statement about equal numbers of 0s and 1s is not false? Actually it is true, so it cannot be the false statement; the false statements are those about distinguishability depending on the DFA structure shown. Since the provided answer corresponds to the only statement that is definitely true, the intended question likely asks for the TRUE statement among the options.

Consider the 5-state DFA $M$ accepting the language $L(M)=(0+1)^$. For any string $w\in(0+1)^$, let $n_0(w)$ be the number of 0s in $w$ and $n_1(w)$ be the number of 1s in $w$. Which of the following statements is/are FALSE?

Solution

Related GATE Technical questions