Reducing the number of solutions of NP functions
Journal of Computer and System Sciences
Reducing the Number of Solutions of NP Functions
MFCS '00 Proceedings of the 25th International Symposium on Mathematical Foundations of Computer Science
Query-monotonic Turing reductions
Theoretical Computer Science
Fine hierarchies and m-reducibilities in theoretical computer science
Theoretical Computer Science
Query-monotonic turing reductions
COCOON'05 Proceedings of the 11th annual international conference on Computing and Combinatorics
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We study the effect of query order on computational power and show that ${\rm P}^{{\rm BH}_j[1]:{\rm BH}_k[1]}$\allowbreak---the languages computable via a polynomial-time machine given one query to the $j$th level of the boolean hierarchy followed by one query to the $k$th level of the boolean hierarchy---equals ${\rm R}_{{j+2k-1}{\scriptsize\mbox{-tt}}}^{p}({\rm NP})$ if $j$ is even and $k$ is odd and equals ${\rm R}_{{j+2k}{\scriptsize\mbox{-tt}}}^{p}({\rm NP})$ otherwise. Thus unless the polynomial hierarchy collapses it holds that, for each $1\leq j \leq k$, ${\rm P}^{{\rm BH}_j[1]:{\rm BH}_k[1]} = {\rm P}^{{\rm BH}_k[1]:{\rm BH}_j [1]} \iff (j=k) \lor (j\mbox{ is even}\, \land k=j+1)$. We extend our analysis to apply to more general query classes.