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The Analytic PolynomialTime Hierarchy
 Mathematical Logic Quaterly
, 1997
"... Motivated by results on interactive proof systems we investigate an 98hierarchy over P using word quantifiers as well as two types of set quantifiers. This hierarchy, which extends the (arithmetic) polynomialtime hierarchy, is called the analytic polynomialtime hierarchy. It is shown that every ..."
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Cited by 3 (2 self)
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Motivated by results on interactive proof systems we investigate an 98hierarchy over P using word quantifiers as well as two types of set quantifiers. This hierarchy, which extends the (arithmetic) polynomialtime hierarchy, is called the analytic polynomialtime hierarchy. It is shown
Hierarchies from Fluxes in String Compactifications
, 2002
"... Warped compactifications with significant warping provide one of the few known mechanisms for naturally generating large hierarchies of physical scales. We demonstrate that this mechanism is realizable in string theory, and give examples involving orientifold compactifications of IIB string theory a ..."
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Cited by 724 (33 self)
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Warped compactifications with significant warping provide one of the few known mechanisms for naturally generating large hierarchies of physical scales. We demonstrate that this mechanism is realizable in string theory, and give examples involving orientifold compactifications of IIB string theory
Electronic Markets and Electronic Hierarchies
 Communications of the ACM
, 1987
"... This paper analyzes the fundamental changes in market structures that may result from the increasing use of information technology. First, an analytic framework is presented and its usefulness is demonstrated in explaining several major historical changes in American business structures. Then, the f ..."
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Cited by 684 (11 self)
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, the framework is used to help explain how electronic markets and electronic hierarchies will allow closer integration of adjacent steps in the value added chains of our economy. The most surprising prediction is that information technology will lead to an overall shift toward proportionately more coordination
PP IS AS HARD AS THE POLYNOMIALTIME HIERARCHY*
"... Abstract. In this paper, two interesting complexity classes, PP and P, are compared with PH, the polynomialtime hierarchy. It is shown that every set in PH is polynomialtime Turing reducible to a set in PP, and PH is included in BP. 0)P. As a consequence of the results, it follows thatPPPH (or 03P ..."
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P__ _ PH) implies a collapse of PH. A stronger result is also shown: every set in PP(PH) is polynomialtime Turing reducible to a set in PP. Key words, polynomialtime hierarchy, probabilistic Turing machine, polynomialtime Turing reductions, parity, randomized reduction
PolynomialTime Hierarchy on Randomized Machines
"... 1 Introduction Proving lower bounds remains one of the most challenging tasks in computationalcomplexity. Satisfiability, the seminal NPcomplete problem, is particularly unyielding in this respect. While we believe that any algorithm for satisfiabilitytakes time linear exponential in the number of ..."
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of variables in the formula, we have been unable to prove superlinear time lower bounds on random access machinesdespite several decades of effort. Additionally, problems complete for higher levels of the polynomialtime hierarchy, while not receiving as much attention, havealso resisted nontrivial time lower
Polynomial time approximation schemes for Euclidean TSP and other geometric problems
 In Proceedings of the 37th IEEE Symposium on Foundations of Computer Science (FOCS’96
, 1996
"... Abstract. We present a polynomial time approximation scheme for Euclidean TSP in fixed dimensions. For every fixed c � 1 and given any n nodes in � 2, a randomized version of the scheme finds a (1 � 1/c)approximation to the optimum traveling salesman tour in O(n(log n) O(c) ) time. When the nodes a ..."
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Cited by 399 (3 self)
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Abstract. We present a polynomial time approximation scheme for Euclidean TSP in fixed dimensions. For every fixed c � 1 and given any n nodes in � 2, a randomized version of the scheme finds a (1 � 1/c)approximation to the optimum traveling salesman tour in O(n(log n) O(c) ) time. When the nodes
A Robot Exploration and Mapping Strategy Based on a Semantic Hierarchy of Spatial Representations
 JOURNAL OF ROBOTICS AND AUTONOMOUS SYSTEMS
, 1991
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Algorithms for Quantum Computation: Discrete Logarithms and Factoring
, 1994
"... A computer is generally considered to be a universal computational device; i.e., it is believed able to simulate any physical computational device with a increase in computation time of at most a polynomial factor. It is not clear whether this is still true when quantum mechanics is taken into consi ..."
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Cited by 1103 (7 self)
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A computer is generally considered to be a universal computational device; i.e., it is believed able to simulate any physical computational device with a increase in computation time of at most a polynomial factor. It is not clear whether this is still true when quantum mechanics is taken
Simulating Physics with Computers
 SIAM Journal on Computing
, 1982
"... A digital computer is generally believed to be an efficient universal computing device; that is, it is believed able to simulate any physical computing device with an increase in computation time of at most a polynomial factor. This may not be true when quantum mechanics is taken into consideration. ..."
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Cited by 601 (1 self)
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A digital computer is generally believed to be an efficient universal computing device; that is, it is believed able to simulate any physical computing device with an increase in computation time of at most a polynomial factor. This may not be true when quantum mechanics is taken into consideration
KodairaSpencer theory of gravity and exact results for quantum string amplitudes
 Commun. Math. Phys
, 1994
"... We develop techniques to compute higher loop string amplitudes for twisted N = 2 theories with ĉ = 3 (i.e. the critical case). An important ingredient is the discovery of an anomaly at every genus in decoupling of BRST trivial states, captured to all orders by a master anomaly equation. In a particu ..."
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Cited by 545 (60 self)
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We develop techniques to compute higher loop string amplitudes for twisted N = 2 theories with ĉ = 3 (i.e. the critical case). An important ingredient is the discovery of an anomaly at every genus in decoupling of BRST trivial states, captured to all orders by a master anomaly equation. In a
Results 1  10
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