GATE CS 2015 Set 1 Q.19 (CS Q.9): Process Synchronization and Concurrency

The following two functions P1 and P2 that share a variable B with an initial value of $2$ execute concurrently.

P1() {
    C = B - 1;
    B = 2 * C;
}

P2() {
    D = 2 * B;
    B = D - 1;
}

The number of distinct values that B can possibly take after the execution is _____.

Your answer

Official answer and solution

Official answer: 3
From: Official GATE 2015 answer key

Solution

Trace all valid instruction interleavings of concurrent processes P1 and P2 sharing variable B initialized to 2.

Let initial $B = 2$ .
Process P1 statements:

$S_1$ : $C = B - 1$
$S_2$ : $B = 2 * C$

Process P2 statements:

$S_3$ : $D = 2 * B$
$S_4$ : $B = D - 1$

Tracing possible execution sequences:

$P1$ then $P2$ ( $S_1 \to S_2 \to S_3 \to S_4$ ):
$S_1$ : $C = 2 - 1 = 1$ .
$S_2$ : $B = 2 \times 1 = 2$ .
$S_3$ : $D = 2 \times 2 = 4$ .
$S_4$ : $B = 4 - 1 = 3$ .
Final $B = 3$ .
$P2$ then $P1$ ( $S_3 \to S_4 \to S_1 \to S_2$ ):
$S_3$ : $D = 2 \times 2 = 4$ .
$S_4$ : $B = 4 - 1 = 3$ .
$S_1$ : $C = 3 - 1 = 2$ .
$S_2$ : $B = 2 \times 2 = 4$ .
Final $B = 4$ .
$S_1 \to S_3 \to S_4 \to S_2$ :
$S_1$ : $C = 2 - 1 = 1$ .
$S_3$ : $D = 2 \times 2 = 4$ .
$S_4$ : $B = 4 - 1 = 3$ .
$S_2$ : $B = 2 \times C = 2 \times 1 = 2$ .
Final $B = 2$ .
$S_3 \to S_1 \to S_2 \to S_4$ :
$S_3$ : $D = 2 \times 2 = 4$ .
$S_1$ : $C = 2 - 1 = 1$ .
$S_2$ : $B = 2 \times 1 = 2$ .
$S_4$ : $B = D - 1 = 4 - 1 = 3$ .
Final $B = 3$ .
$S_1 \to S_3 \to S_2 \to S_4$ :
$S_1$ : $C = 1, S_3$ : $D = 4$ .
$S_2$ : $B = 2 \times 1 = 2$ .
$S_4$ : $B = 4 - 1 = 3$ .
Final $B = 3$ .
$S_3 \to S_1 \to S_4 \to S_2$ :
$S_3$ : $D = 4, S_1$ : $C = 1$ .
$S_4$ : $B = 3$ .
$S_2$ : $B = 2 \times 1 = 2$ .
Final $B = 2$ .

The distinct final values that $B$ can take are $\{2, 3, 4\}$ .
The count of distinct values is 3.

Final answer

Common trap

Testing only the two strictly sequential executions (yielding 3 and 4) and overlooking the interleaved case where P1 overwrites B last to leave it at 2.

The answer is the one in the official GATE answer key. The solution is this site's own explanation.

Source

Paper: GATE 2015 Computer Science and Information Technology (CS) Session 1
Question: 19 of 65, printed as CS Q.9
Section: Computer Science and Information Technology

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