Consider the following deterministic finite automaton (DFA).

The number of strings of length 8 accepted by  the above automaton is __________

For a string w, we define wR to be the reverse of w. For example, if w = 01101 then wR = 10110.

Which of the following languages is/are context-free?

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.

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