GATE CSE 2024 Set 1 | Finite Automata and Regular Language Question 6 | Theory of Computation

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GATE CSE 2024 Set 1

Numerical

-0

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 ________

Your input ____

GATE CSE 2023

Numerical

-0

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 ___________.

Your input ____

GATE CSE 2021 Set 2

MCQ (More than One Correct Answer)

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Which of the following regular expressions represent(s) the set of all binary numbers that are divisible by three? Assume that the string ∈ divisible by three.

(0 + 1(01*0)*1)*

(0*(1(01*0)*1)*)*

(0 + 11 + 10(1 + 00)*01)*

( 0+ 11 + 11(1 + 00)*00)*

GATE CSE 2021 Set 2

Numerical

-0

Consider a network using the pure ALOHA medium access control protocol, where each frame is of length 1,000 bits. The channel transmission rate is 1 Mbps (= 106 bits per second). The aggregate number of transmissions across all the nodes (in-cluding new frame transmissions and retransmitted frames due to collisions) is modelled as a Poisson process with a rate of 1,000 frames per second. Throughput is defined as the average number of frames successfully transmitted per second. The throughput of the network (rounded to the nearest integer) is

Your input ____