Query Order and the Polynomial Hierarchy

TL;DR

This paper explores how the sequence of information access impacts the polynomial hierarchy, revealing that while the hierarchy levels are order-oblivious, ordered query classes can form new hierarchy levels unless collapse occurs.

Contribution

It is the first study to analyze query order effects on the polynomial hierarchy, establishing order-obliviousness and the potential for new hierarchy levels.

Findings

Polynomial hierarchy levels are order-oblivious.

Ordered query classes can form new levels unless the hierarchy collapses.

All leaf language classes inherit order-obliviousness results.

Abstract

Hemaspaandra, Hempel, and Wechsung [cs.CC/9909020] initiated the field of query order, which studies the ways in which computational power is affected by the order in which information sources are accessed. The present paper studies, for the first time, query order as it applies to the levels of the polynomial hierarchy. We prove that the levels of the polynomial hierarchy are order-oblivious. Yet, we also show that these ordered query classes form new levels in the polynomial hierarchy unless the polynomial hierarchy collapses. We prove that all leaf language classes - and thus essentially all standard complexity classes - inherit all order-obliviousness results that hold for P.