Motivated by results on interactive proof systems we investigate an 9-8-hierarchy over P using word quantifiers as well as two types of set quantifiers. This hierarchy, which extends the (arithmetic) polynomial-time hierarchy, is called the analytic polynomial-time hierarchy. It is shown

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

, 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

P__ _ PH) implies a collapse of PH. A stronger result is also shown: every set in PP(PH) is polynomial-time Turing reducible to a set in PP. Key words, polynomial-time hierarchy, probabilistic Turing machine, polynomial-time Turing reductions, parity, randomized reduction

of variables in the formula, we have been unable to prove super-linear time lower bounds on random access machinesdespite several decades of effort. Additionally, problems complete for higher levels of the polynomial-time hierarchy, while not receiving as much attention, havealso resisted nontrivial time lower

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

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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

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

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