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Two queries
 In CCC
, 1999
"... We consider the question whether two queries to SAT are as powerful as one query. We show that if P NP�℄� P NP�℄then Locally either NP�coNP or NP has polynomialsize circuits. ..."
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Cited by 33 (6 self)
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We consider the question whether two queries to SAT are as powerful as one query. We show that if P NP�℄� P NP�℄then Locally either NP�coNP or NP has polynomialsize circuits.
Query order in the polynomial hierarchy
 Journal of Universal Computer Science
, 1998
"... Hemaspaandra, Hempel, and Wechsung [HHW] 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 polynomia ..."
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Cited by 9 (7 self)
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Hemaspaandra, Hempel, and Wechsung [HHW] 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. P C:D denotes the class of languages computable by a polynomialtime machine that is allowed one query to C followed by one query to D [HHW]. We prove that the levels of the polynomial hierarchy are orderoblivious: P Σp j:Σp k = P Σp k:Σp j. 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 orderobliviousness results that hold for P. 1
Bounded queries, approximations and the Boolean hierarchy
 Electronic Colloquium on Computational Complexity
, 1997
"... This paper investigates nondeterministic bounded query classes in relation to the complexity of NPhard approximation problems and the Boolean Hierarchy. Nondeterministic bounded query classes turn out be rather suitable for describing the complexity of NPhard approximation problems. The results in ..."
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Cited by 7 (3 self)
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This paper investigates nondeterministic bounded query classes in relation to the complexity of NPhard approximation problems and the Boolean Hierarchy. Nondeterministic bounded query classes turn out be rather suitable for describing the complexity of NPhard approximation problems. The results in this paper take advantage of this machinebased model to prove that in many cases, NPapproximation problems have the upward collapse property. That is, a reduction between NPapproximation problems of apparently different complexity at a lower level results in a similar reduction at a higher level. For example, if MaxClique reduces to (log n)approximating MaxClique using manyone reductions, then the Traveling Salesman Problem (TSP) is equivalent to MaxClique under manyone reductions. Several upward collapse theorems are presented in this paper. The proofs of these theorems rely heavily on the machinery provided by the nondeterministic bounded query classes. In fact, these results depend on a surprising connection between the Boolean Hierarchy and nondeterministic bounded query classes.
RSN 1tt (NP) distinguishes robust manyone and Turing completeness
 Theory of Computing Systems
, 1998
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Selfspecifying machines
, 1998
"... We study the computational power of machines that specify their own acceptance types, and show that they accept exactly the languages that ≤ #P mreduce to NP sets. A natural variant accepts exactly the languages that ≤ #P mreduce to P sets. We show that these two classes coincide if and only if P ..."
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We study the computational power of machines that specify their own acceptance types, and show that they accept exactly the languages that ≤ #P mreduce to NP sets. A natural variant accepts exactly the languages that ≤ #P mreduce to P sets. We show that these two classes coincide if and only if P #P[1] = P #P[1]:NP[O(1)] , where the latter class denotes the sets acceptable via at most one question to #P followed by at most a constant number of questions to NP.