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Topic: Exponential hierarchy

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In the News (Fri 17 Feb 12)

EXECUTIVE POWER

Iran

ANALYSIS

Pakistan

Family compact

	Cheops: A Compact Explorer For Complex Hierarchies
		The total drawing length for the hierarchies are calculated assuming 1.2 centimeter squares, drawn side by side, for the last level of the hierarchy.
		The selection technique allows the user to set a reference state of the hierarchy, or selection of a node, and the resulting structure of the sub-hierarchy is revealed by the subtraction of the branches outside the selection.
		Internally, the logical nodes are a hierarchy of objects, accessed through paths relative to any node (usually the root.) For example, the second child of the first child of the root would be designated by the string "01" (The root itself is the empty string.) The first child of that node would be "010".
	maparent.ca /paper.html (4544 words)

	[No title]
		A new framework for solving the hierarchy problem was recently proposed which does not rely on low energy supersymmetry or technicolor.
		The finite radius of the transverse dimensions follows from Einstein's equation, and is exponentially large compared with the scales associated with the 3-brane.
		There are two 3-branes, and the mass scale for fields that propagate on one of the 3-branes is exponentially suppressed relative to the fundamental scale of theory, which is taken to be the Planck mass, M_Pl.
	www.mit.edu /~nleonard/x/xcompile.html (3151 words)

	Fundamental Theory Group:Strings and M-Theory
		This exponential hierarchy is technically unnatural in particle physics, since in general, the effects of renormalization are to make the observable values of such scales much closer in size.
		In this picture the hierarchy problem is is no longer a disparity between mass scales, and instead becomes an issue of length scales.
		Thus, the problem of understanding the hierarchy between the Planck and weak scales now becomes that of understanding why extra dimensions are stabilized at a linear size (~1 mm, for example) large with respect to the fundamental length scale M*-1.
	www-hl.syr.edu /depts/physics/FTGCosmology.htm (2558 words)

	Exponential Data Compression - Frdcsa.onshore.net (Site not responding. Last check: 2007-10-12)
		To avoid having to deal with excrutiatingly large hierarchies, one can just re-partition the original file into longer bit word sizes, and consider building small chains of those nodes (nodes = binary bit words of whatever length), and make a set of compression hierarchies out of each of those.
		Exponential Data Compression is what I was referring to before as R.C.B.L.G.O. It utilizes the hierarchical Sine Spiral Graphing of polynomials on a recursive orthogonal numberline, (see other papers and WIKI) and the fact that when one variable is multiplied by another variable (or an exponent), it creates a perpendicular dimension on a spiraling curvature.
		Then on each exponential level, sequential words from the previous level get bitshifted, and the word size grows by one bit per level in case the bitshifting of the two sequential words (of equal size) outgrows the word size, but that is a trivial detail that doesn't matter in the end.
	frdcsa.onshore.net /mediawiki/index.php/Exponential_Data_Compression (635 words)

	CJTCS Volume 1996 Article 4 (Site not responding. Last check: 2007-10-12)
		The complexity of the language generated by a grammar depends crucially on whether the position valuation is steady or not.
		On the other hand, for every steady position valuation, the class of languages generated corresponds to a level of the hierarchy of exponential time-bounded languages in CSL.
		The hierarchy of exponential time-bounded languages in CSL collapses.
	cjtcs.cs.uchicago.edu /articles/1996/4/contents.html (213 words)

	faculty
		A very attractive solution to the hierarchy problem, known as the Randall-Sundrum scenario, relies on the high curvature of a 5-dimensional spacetime.
		This setup explains the exponential hierarchy between the Planck and electroweak scales as the result of a gravitational red-shift when different positions along the fifth dimension are compared.
		If the standard model gauge and fermions fields propagate in the 5-dimensional bulk, these scenarios become consistent with gauge coupling unification, and also allow an understanding of the observed fermion mass hierarchies as the result of the localization of the fermions along the extra dimension.
	www.columbia.edu /cu/physics/fac-bios/Ponton/faculty.html (419 words)

	Computational Complexity; Problem Hierarchy (Site not responding. Last check: 2007-10-12)
		Problems of exponential complexity are "solved" using approximate methods that are of polynomial complexity.
		Theorem proving is an example of a problem of exponential complexity while proof checking is of linear (polynomial) complexity.
		If there are an unlimited number of computers, then some exponential complexity problems may be solved in polynomial time.
	cs.wwc.edu /~aabyan/Theory/complexity.html (1650 words)

	Anisotropy, lacunarity, upscaled conductivity, and its covariance in multiscale random fields with truncated power ...
		Di Federico and Neuman [1997] have demonstrated that the power variogram and associated spectra of a statistically isotropic fractal field can be constructed as a weighted integral from zero to infinity (an infinite hierarchy) of exponential or Gaussian variograms and spectra of mutually uncorrelated fields (modes) that are homogeneous and isotropic.
		We show in this paper that the same holds true when the field and its constituent modes are statistically anisotropic, provided the ratios between principal integral (spatial correlation) scales are the same for all modes.
		A low-frequency cutoff renders the truncated hierarchy homogeneous.
	math.lanl.gov /~dmt/Publications/federico-1999-anisotropy.shtml (477 words)

	Ordinal numbers
		There is a correspondence between the hierarchy of ordinal arithmetic and functions on the integers that increase more rapidly.
		With multiplication as a base, each level of the exponential hierarchy is iteration of the previous level.
		One can generalize from the entire exponential hierarchy to create a function that is not in the exponential hierarchy and grows faster than any exponential function.
	www.mtnmath.com /whatth/node36.html (296 words)

	Dieter van Melkebeek - Research on Computational Complexity Theory
		A similar situation holds for the polynomial-time hierarchy, a tower of complexity classes within PSPACE the first two levels of which are P and NP.
		Such hierarchies have been established for any reasonable model of computation that is syntactic, i.e., for which there exists a computable enumeration of all machines in the model.
		Torenvliet established that large complexity classes like doubly exponential space have complete languages that are not autoreducible, whereas the complete languages of smaller classes like exponential time all share the property of autoreducibility.
	www.cs.wisc.edu /~dieter/Research/complexity.html (2966 words)

	Complexity Zoo - Qwiki
		Similar to TreeBQP except that the quantum computer's state at each time step is restricted to being exponentially close to a state in AmpP (that is, a state for which the amplitudes are computable by a classical polynomial-size circuit).
		However, [Bar02] and [FS04] have shown hierarchy theorems for BPP with a small amount of advice.
		Proving a stronger time hierarchy theorem for BPTIME is a longstanding open problem; see [BH97] for details.
	qwiki.caltech.edu /wiki/Complexity_Zoo (6750 words)

	The Reference Frame: Savas' colloquium
		However, Savas encouraged others to look for a truly scientific explanation of the hierarchy problem and perhaps also the cosmological constant problem.
		Bert Halperin noted that he had a solution to the cosmological constant problem, but based on obvious reasons, he could not have said what it was in front of Savas.
		If it is hard for the alpha particle to get out because of the barrier, consider the reversed process, it should also be exponentially hard for an alpha particle to penetrate the barrier and get in.
	motls.blogspot.com /2005/04/savas-colloquium.html (2087 words)

	ExpoMapNode class Reference
		This class represents a node whose rotation is a exponential map.
		Initialises the exponential map node by a quaternion quat.
		Constructor that sets up the rotation, and calls the TransformNode constructor, passing the name nname of the node, a pointer to its parent nparent, a Boolean active indicating whether the node is active, the initial value rot of its rotation, the order of the rotations dofs_in, and finally, the node number nodeNumber.
	ligwww.epfl.ch /~lorna/doxygen/FittingGraph/classExpoMapNode.html (635 words)

	Average-Time Hierarchies
		To study average-case hierarchies in the framework of Definition 2.1, a finer distinction between average time, namely, not just between average polynomial and super-polynomial, is needed.
		It is therefore possible to prove an average-case hierarchy result as tight as in the worst case.
		A slightly tighter hierarchy can also be obtained under nonuniform distributions [SY96].
	www.uncg.edu /mat/avg/avgcomp/node19.html (365 words)

	Bug ID: 5085626 Exponential performance regression in AWT components (multiple monitors)
		In the AWT program, the event dispatch thread is * frozen while all of the surface datas are being recreated in the hierarchy * (in Win32SurfaceData.initOps).
		ACTUAL - Exponential performance degredation depending on number of levels in the component hierarchy.
		Unless otherwise licensed, code in all technical manuals herein (including articles, FAQs, samples) is provided under this License.
	bugs.sun.com /bugdatabase/view_bug.do?bug_id=5085626 (592 words)

	[No title] (Site not responding. Last check: 2007-10-12)
		A set is autoreducible if it can be reduced to itself by a Turing machine that does not ask its own input to the oracle.
		We use autoreducibility to separate the polynomial-time hierarchy from exponential space by showing that all Turing-complete sets for certain levels of the exponential-time hierarchy are autoreducible but there exists some Turing-complete set for doubly exponential space that is not.
		In particular, if we could settle the question as to whether all Turing-complete sets for doubly exponential time are autoreducible, we would separate either polynomial time from polynomial space, and nondeterministic logarithmic space from nondeterministic polynomial time, or else the polynomial-time hierarchy from exponential time.
	www.cs.wisc.edu /~dieter/Research/auto.html (203 words)

	Stratified exponential families: Graphical models and model selection, Dan Geiger, David Heckerman, Henry King, ...
		We describe a hierarchy of exponential families which is useful for distinguishing types of graphical models.
		Directed acyclic graphical (DAG) models and chain graphs with no hidden variables, includ ing DAG models with several families of local distributions, are curved exponential families (CEFs).
		We also show that this hierarchy of exponential families is noncollapsing with respect to graphical models by providing a graphical model which is a CEF but not a LEF and a graphical model that is a SEF but not a CEF.
	projecteuclid.org /Dienst/UI/1.0/Summarize/euclid.aos/1009210550 (870 words)

	Bug ID: 4686431 javac requires exponential time to attribute methods in a large hierarchy
		Bug ID: 4686431 javac requires exponential time to attribute methods in a large hierarchy
		..For large inheritance hierarchies, javac appears to require something like exponential time to compile.
		This isn't exactly a bug in the sense of incorrect behavior, but it isn't very nice either.
	bugs.sun.com /bugdatabase/view_bug.do?bug_id=4686431 (506 words)

	Selected Publications (Site not responding. Last check: 2007-10-12)
		Mocas, ``A Note on the Relationship of BPP and RP to Exponential Time Classes'', Portland State University Technical Report TR02-1, 2002.
		Mocas, ``Using Bounded Query Classes to Separate Classes in the Exponential Time Hierarchy from Classes in PH'', Theoretical Computer Science 158,1996, pp.
		Homer and S. Mocas, ``Nonuniform Lower Bounds for Exponential Time Classes'', Proceedings from the 20th International Symposium on Mathematical Foundations of Computer Science August, 1995.
	web.cecs.pdx.edu /~sarah/pubs.html (258 words)

	UofT Department of Computer Science Ph.D. Theses 2005-06
		The second-order viewpoint of Zambella and Cook associates second-order theories of bounded arithmetic with various complexity classes by studying the definable functions of strings, rather than numbers.
		This approach simplifies presentation of the theories and their propositional translations, and furthermore is applicable to complexity classes that previously had no corresponding theories.
		We adapt this viewpoint to large complexity classes from the exponential-time hierarchy by adding a third sort, intended to represent exponentially long strings (``superstrings''), and capable of coding, for example, the computation of an exponential-time Turing machine.
	www.cs.toronto.edu /DCS/Grad/Theses/05-06PhD.html (1461 words)

	SCI-BITES: Hot Paper in Physics
		The weak scale is generated from the Planck scale through an exponential hierarchy.
		However, this exponential arises not from gauge interactions but from the background metric (which is a slice of AdS5 spacetime).
		We demonstrate a simple explicit example of this mechanism with two 3-branes, one of which contains the standard model fields.
	www.in-cites.com /research/2001/june_11_2001-3.html (378 words)

	Super-Polynomial versus Half-Exponential Circuit Size in the Exponential Hierarchy - Miltersen, Vinodchandran, Watanabe ... (Site not responding. Last check: 2007-10-12)
		Super-Polynomial versus Half-Exponential Circuit Size in the Exponential Hierarchy (1999)
		Informally, a function f is said to be half-exponential when f f is exponential.
		Super-polynomial versus half-exponential circuit size in the exponential hierarchy.
	citeseer.ist.psu.edu /354542.html (565 words)

	Computational Complexity: Extreme Oracles
		P≠NP, the polynomial-time hierarchy is infinite, PP is not in P
		Relative to this oracle ZPP=⊕EXP and the isomorphism conjecture holds (all NP-complete problems are reducible to each other via invertible bijections).
		The polynomial-time hierarchy collapses to P and yet the exponential hierarchy sits inside &oplus;P. P=⊕P and BPP=EXP
	weblog.fortnow.com /2005/08/extreme-oracles.html (724 words)

	Information and Computation Bibliography (Site not responding. Last check: 2007-10-12)
		With probability one, a random oracle separates PSPACE from the polynomial-time hierarchy.
		The Boolean hierarchy and the polynomial hierarchy: a closer connection.
		The polynomial time hierarchy collapses if the Boolean hierarchy collapses.
	theory.lcs.mit.edu /~iandc/References/gasarchhh1993:72.html (475 words)

	ECCC Report TR04-007 and related Papers (Site not responding. Last check: 2007-10-12)
		Abstract: It is known cite{BHZ87} that if every language in coNP has a constant-round interactive proof system, then the polynomial hierarchy collapses.
		We show that if every set in coNP has a polylogarithmic-round interactive protocol then the exponential hierarchy collapses to the third level.
		In order to prove this, we obtain an exponential version of Yap's result cite{yap83}, and improve upon an exponential version of the Karp-Lipton theorem cite{kl80}, obtained first by Buhrman and Homer cite{bh92}.
	eccc.hpi-web.de /eccc-reports/2004/TR04-007/index.html (207 words)

	No Title
		Lower Bounds for the Low Hierarchy, E. Allender and L. Hemachandra, Journal of the ACM, V. 39, #1, pp.
		The Boolean Hierarchy II: Applications, J. Cai, T. Gundermann, J. Hartmanis, L. Hemachandra, V. Sewelson, K. Wagner, and G. Wechsung, SIAM Journal on Computing, V. pp.
		The Boolean Hierarchy I: Structural Properties, J. Cai, T. Gundermann, J. Hartmanis, L. Hemachandra, V. Sewelson, K. Wagner, and G. Wechsung, SIAM Journal on Computing, V. 17, #6, pp.
	www.cs.rochester.edu /u/lane/resume-book-journal.html (1126 words)

	The Trouble with Checked Exceptions
		The trouble begins when you start building big systems where you're talking to four or five different subsystems.
		Now, each time you walk up the ladder of aggregation, you have this exponential hierarchy below you of exceptions you have to deal with.
		You end up having to declare 40 exceptions that you might throw.
	www.artima.com /intv/handcuffs3.html (499 words)

	Annotated bibliography of papers by Christopher Meek
		exponentially fast as one increases the number of bits used to
		We describe a hierarchy of exponential families which is useful
		exponential families is non-collapsing with respect to graphical
	research.microsoft.com /~meek/mypapers.htm (4666 words)

	Switch 4007 Implementation Guide
		Ethernet is a standardized, switched, packet-based network that supports an exponential hierarchy of three line speeds:
		All speeds of Ethernet are based on an IEEE 802.3 standard protocol called Carrier Sense Multiple Access with Collision Detection (CSMA/CD), which controls network access.
		The hierarchy of Ethernet, Fast Ethernet, and Gigabit Ethernet technologies offers these additional network benefits:
	support.3com.com /infodeli/tools/switches/4000/4007/13673/9i3ether.htm (2335 words)

	ECCC, Volume 11
		Exponential Separation of Quantum and Classical One-Way Communication Complexity.
		Exponential lower bounds for the running time of DPLL algorithms on satisfiable formulas.
		Exponential time reductions and sparse languages in NEXP.
	www.acm.org /sigs/sigmod/dblp/db/journals/eccc/eccc11.html (675 words)

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