Discussion
A set of processors P1, P2, ……, Pk can execute in parallel if Bernstein's conditions are satisfied on a pairwise basis; that is P1 || P2 || P3 || ….. || Pk if and only if :
Answer: A
Bernstein's conditions are checked pairwise, and the processors P1 to Pk can execute in parallel if and only if every pair of different processors satisfies them, that is Pi || Pj for all i not equal to j, option (A). Since the relation is symmetric, it is enough that all distinct pairs are independent. The conditions i = j+1 in (B) cover only consecutive pairs, and i less than or equal to j in (C) and i greater than or equal to j in (D) include i = j, where a processor would be compared with itself, which is not a pair of different processors, and each covers only half of the pairs.
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