Query Order

TL;DR

This paper investigates how the order of queries affects computational power, establishing precise equivalences between certain query classes and levels of the boolean hierarchy, with implications for the polynomial hierarchy.

Contribution

It characterizes the computational power of query orderings in the boolean hierarchy and extends the analysis to more general query classes.

Findings

Query order impacts computational class equivalences.

Established exact class equalities based on query positions.

Extended analysis to broader query classes.

Abstract

We study the effect of query order on computational power, and show that $\pjk$-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 $\redttnp{j+2k-1}$ if j is even and k is odd, and equals $\redttnp{j+2k}$ otherwise. Thus, unless the polynomial hierarchy collapses, it holds that for each $1\leq j \leq k$: $\pjk = \pkj \iff (j=k) \lor (j{is even} \land k=j+1)$. We extend our analysis to apply to more general query classes.