A variable x is said to be live at a statement $${S_i}$$ in a programif the following three conditions hold simultaneously:

i. There exists a statement $${S_j}$$ that uses x
ii. There is a path from $${S_i}$$ to $${S_j}$$ in the flow graph corresponding to the program
iii. The path has no intervening assignment to x including at $${S_i}$$ and $${S_j}$$

The variables which are live both at the statement in basic block 2 and at the statement in basic block 3 of the above control flow graph are

The least number of temporary variables required to create a three-address code in static single assignment form for the expression $$q + r / 3 + s - t * 5 + u * v/w$$ is _______________.

Consider a LAN with four nodes S₁, S₂, S₃ and S₄. Time is divided into fixed-size slots, and a node can begin its transmission only at the beginning of a slot. A collision is said to have occurred if more than one node transmit in the same slot. The probabilities of generation of a frame in a time slot by S₁, S₂, S₃ and S₄ are 0.1, 0.2, 0.3 and 0.4, respectively. The probability of sending a frame in the first slot without any collision by any of these four stations is _________.

Suppose that the stop-and-wait protocol is used on a link with a bit rate of 64 kilobits per second and 20 milliseconds propagation delay. Assume that the transmission time for the acknowledgment and the processing time at nodes are negligible. Then the minimum frame size in bytes to achieve a link utilization of at least 50% is _________.