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Bounded query classes and the difference hierarchy

Richard Beigel, William I. Gasarch, Louise Hay
1989 Archive for Mathematical Logic  
We de ne a hierarchy of sets (and a corresponding hierarchy of degrees) that are reducible to A based on bounding the number of queries to A that an oracle machine can make.  ...  When A is the halting problem K our hierarchy of sets interleaves with the di erence hierarchy on the r.e. sets in a logarithmic way; this follows from a tradeo between the number of parallel queries and  ...  Acknowledgments The authors would like to thank Robert Floyd, John Gill, and Jim Owings for helpful comments.  ... 
doi:10.1007/bf01620618 fatcat:nafueh2ainbpjbvmtc3xxjwuaq

Bounded queries to SAT and the Boolean hierarchy

Richard Beigel
1991 Theoretical Computer Science  
., Bounded queries to SAT and the Boolean hierarchy, Theoretical Computer Science 84(1991)199-223.  ...  We will show how the difference hierarchy and the bounded query hierarchies interleave. Theorem 4.5. (i) Zf % is any class of languages then PZttG P;.rC P&r,.,,.  ...  Each element of a bounded query hierarchy is called a bounded query class. See [9, lo] for more on bounded query classes relative to nonrecursive oracles.  ... 
doi:10.1016/0304-3975(91)90160-4 fatcat:q5kfoes22jb3lk3hzwpntdywxa

Space-bounded hierarchies and probabilistic computations

Walter L. Ruzzo, Janos Simon, Martin Tompa
1984 Journal of computer and system sciences (Print)  
Third, we give a new definition of space-bounded oracle machines, and use it to define a space-bounded "oracle hierarchy" analogous to the original definition of the polynomial time hierarchy.  ...  However, the entire log n space "oracle hierarchy" is still contained in bounded-error probabilistic space log n.  ...  The second major difference in the behavior of the time versus space-bounded complexity classes is the (presumed) separation of the alternation and oracle hierarchies in the space-bounded case.  ... 
doi:10.1016/0022-0000(84)90066-7 fatcat:bvcg33bozrbc7beb5fusesbngu

New developments in structural complexity theory

J. Hartmanis
1990 Theoretical Computer Science  
The Query Hierarchy, QH, is given by can be shown that the two hierarchies, BH, and QH. ale intertwined and therefore BH is finite if and only if QH is finite [4-Y].  ...  It uses relativization to clarify the power uf different access mechanisms to information, to investigate possible relationships among complexity classes and to try to assess the difficulty of unsolved  ...  Next, we consider the Boolean hierarchy and the Query hierarchy.  ... 
doi:10.1016/0304-3975(90)90191-j fatcat:b32wvwbx4jcw3jmuinbslhk2ii

APPROXIMATE INFORMATION FILTERING WITH MULTIPLE CLASSIFICATION HIERARCHIES

HEINER STUCKENSCHMIDT
2002 International Journal of Computational Intelligence and Applications  
We describe a tool for creating application specific classification hierarchies and introduce an method for approximating Boolean queries over class names across different class hierarchies.  ...  In this paper, we address the problem of filtering information categorized according to different classification hierarchies.  ...  in the hierarchy we query.  ... 
doi:10.1142/s1469026802000634 fatcat:qlqjynxqzvdbtddtqfwvjn2tfi

Relational Databases and Homogeneity in Logics with Counting [chapter]

José María Turull Torres
2002 Lecture Notes in Computer Science  
We define a new hierarchy in the class of computable queries to relational databases, in terms of the preservation of equality of theories in fragments of first order logic with bounded number of variables  ...  We introduce a model of computation of queries to characterize the different layers of our hierarchy which is based on the reflective relational machine of S. Abiteboul, C. Papadimitriou, and V.  ...  Introduction Given a relational database schema, it is natural to think about the whole class of queries which might be computed over databases of that schema.  ... 
doi:10.1007/3-540-45758-5_14 fatcat:as25cqvchzcuraegjgckqhxrla

FCL: A general purpose library for collision and proximity queries

Jia Pan, Sachin Chitta, Dinesh Manocha
2012 2012 IEEE International Conference on Robotics and Automation  
Our library is based on hierarchical representations and designed to perform multiple proximity queries on different model representations.  ...  The set of queries includes discrete collision detection, continuous collision detection, separation distance computation and penetration depth estimation.  ...  The leaf level of the class hierarchy includes nodes for specific types of queries.  ... 
doi:10.1109/icra.2012.6225337 dblp:conf/icra/PanCM12 fatcat:vad7azvlmfgbbjis77uquow7li

Generalized lowness and highness and probabilistic complexity classes

Andrew Klapper
1989 Mathematical Systems Theory  
We also show, with one exception, that containment relations between the bounded probabilistic classes and the polynomial hierarchy are preserved by their low and high counterparts.  ...  We show, for example, that for a bounded probabilistic polynomial time complexity class C = BP Σ P k , LC = HC implies that the polynomial hierarchy collapses to C.  ...  For each k ≥ 0, this gives classes LC and HC for each class C in the bounded probabilistic polynomial hierarchy.  ... 
doi:10.1007/bf02088291 fatcat:cnloc36ujfbopmdus66mldkuhe

Page 2054 of Mathematical Reviews Vol. , Issue 99c [page]

1991 Mathematical Reviews  
Yet we also show that these ordered query classes form new levels in the polynomial hierarchy unless the polynomial hierarchy collapses.  ...  In the polynomial hierarchy, query order never matters. In the Boolean hierarchy, query order sometimes does not matter and, unless the polynomial hierarchy collapses, sometimes does matter.  ... 

Oracles That Compute Values

Stephen Fenner, Steven Homer, Mitsunori Ogihara, Alan Selman
1997 SIAM journal on computing (Print)  
The difference hierarchy for partial functions does not collapse unless the Boolean hierarchy collapses, but, surprisingly, the levels of the difference and bounded query hierarchies do not interleave  ...  Nondeterministic reducibilities, lowness, and the difference hierarchy over NPMV are also studied.  ...  Since the properties of the bounded query hierarchies over NPMV are largely similar to those over NP, one might hope that the same thing happens here-that the difference hierarchy over NPMV and the difference  ... 
doi:10.1137/s0097539793247439 fatcat:kleyx7dchzaylj567c6yr7jedy

Complexity classes between $\Theta _k^P$ and $\Delta _k^P$

J. Castro, C. Seara
1996 RAIRO - Theoretical Informatics and Applications  
Balcâzar and Borja Valles for reading earlier versions of this paper. We would like to thank Eric Allender, Fred Green, Birgit Jenner, Ming-Jye Sheu and Chris Wilson for helpful discussions.  ...  Two anonymous référées deserve our thanks for many valuable suggestions and comments.  ...  Below we show connections between classes of languages recognized by polynomial time oracle machines which make polylog queries to an NP set and other classes defined on different ways.  ... 
doi:10.1051/ita/1996300201011 fatcat:usfnwsieezdt7k2qkua4bvyqoa

Separating classes in the exponential-time hierarchy from classes in PH

Sarah E. Mocas
1996 Theoretical Computer Science  
We are interested in separating classes in the exponential-time hierarchy, EXPH, from classes in the polynomial-time hierarchy, PH.  ...  In this paper we show that, for any fixed integer c, the class of sets accepted in deterministic polynomial time using at most O(n') queries to an NP oracle PNpro(n')l, is a proper subset of NEXP.  ...  Acknowledgements The results in this paper can also be found in [16] .  ... 
doi:10.1016/0304-3975(95)00078-x fatcat:et7kamlqxvevrjwk545wmiabxq

Page 5724 of Mathematical Reviews Vol. , Issue 92j [page]

1992 Mathematical Reviews  
In contrast to this, the two bounded query hierarchies of functions are proper unless P=NP.  ...  The author considers hierarchies of sets and functions which can be computed with a bounded number of queries to an NP oracle. PRE.  ... 

Bounded queries to arbitrary sets

A. Lozano
1996 RAIRO - Theoretical Informatics and Applications  
ACKNOWLEDGEMENTS The author would like to thank José Luis Balcâzar, Richard Beigel, and Ricard Gavaldà for proofreading and the référées for their detailed and helpful comments.  ...  The hierarchy is called the bounded-query hierarchy relative to A, while its parallel counterpart is called the bounded parallel query hierarchy relative to A [4] .  ...  For related results. see [17] . vol. 30 ;n° 2, 1996 Note that it is easy to prove by padding arguments that the bounded-query hierarchy over NE collapses if and only if the bounded-query hierarchy  ... 
doi:10.1051/ita/1996300200911 fatcat:eheogku7gze4pisz4weqztldpy

Page 7808 of Mathematical Reviews Vol. , Issue 97M [page]

1997 Mathematical Reviews  
Summary: “It is known that for any class C closed under union and intersection, the Boolean closure of C, the Boolean hierarchy over C, and the symmetric difference hierarchy over C all are equal.  ...  “In this paper, we compare the bounded-error probabilistic class BPP with the analogous threshold class, BPP,an, and, more gen- erally, we study the structural properties of BPP, an.  ... 
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