Query Order

We study the effect of query order on computational power, and show that Pj k—the languages computable via a polynomial-time machine given one query to the jth level of the boolean hierarchy followed by one query to the kth level of the boolean hierarchy—equals Rpj+2k−1-tt(NP) if j is even and k is odd, and equals Rpj+2k-tt(NP) otherwise. Thus, unless the polynomial hierarchy collapses, it holds that for each 1 ≤ j ≤ k: Pj [1]:BHk[1] = Pkj [1] ⇐⇒ (j = k)∨(j is even ∧ k = j+1). We extend our analysis to apply to more general query classes.