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Summary: Pinpointing Computation with Modular Queries in the Boolean
Hierarchy
Manindra Agrawal
Richard Beigel
Thomas Thierauf
Abstract
A modular query consists of asking how many (modulo m) of k strings belong to a fixed
NP language. Modular queries provide a form of restricted access to an NP oracle. For
each k and m, we consider the class of languages accepted by NP machines that ask a single
modular query. Han and Thierauf [HT95] showed that these classes coincide with levels of
the Boolean hierarchy when m is even or k 2m, and they determined the exact levels.
Until now, the remaining case -- odd m and large k -- looked quite difficult. We pinpoint
the level in the Boolean hierarchy for the remaining case; thus, these classes coincide with
levels of the Boolean hierarchy for every k and m.
In addition we characterize the classes obtained by using an NP(l) acceptor in place of an
NP acceptor (NP(l) is the lth level of the Boolean hierarchy). As before, these all coincide
with levels in the Boolean hierarchy.
Abteilung Theoretische Informatik, Universitšat Ulm, Oberer Eselsberg, 89069 Ulm, Germany. Email:
manindra@informatik.uni-ulm.de. On leave from SPIC Science Foundation, Madras, India. Research supported
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