1
GATE CSE 2024 Set 2
Numerical
+2
-0.66

Let L1 be the language represented by the regular expression b*ab*(ab*ab*)* and L2 = { w ∈ (a + b)* | |w| ≤ 4 }, where |w| denotes the length of string w. The number of strings in L2 which are also in L1 is __________.

2
GATE CSE 2024 Set 1
MCQ (More than One Correct Answer)
+2
-0.66

Consider the 5-state DFA $M$ accepting the language $L(M) \subseteq (0+1)^*$ shown below. For any string $w \in (0+1)^*$ 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 $L(M)$

3
GATE CSE 2024 Set 1
Numerical
+2
-0.66

Consider the following two regular expressions over the alphabet {0,1}:

$$r = 0^* + 1^*$$

$$s = 01^* + 10^*$$

The total number of strings of length less than or equal to 5, which are neither in r nor in s, is ________

4
GATE CSE 2023
Numerical
+2
-0.67

Consider the language L over the alphabet {0, 1}, given below:

$$L = \{ w \in {\{ 0,1\} ^ * }|w$$ does not contain three or more consecutive $$1's\}$$.

The minimum number of states in a Deterministic Finite-State Automaton (DFA) for L is ___________.