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Topic: P (complexity)

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Complexity classes P and NP

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	Computational complexity theory - Wikipedia, the free encyclopedia
		Complexity theory differs from computability theory, which deals with whether a problem can be solved at all, regardless of the resources required.
		The time complexity of a problem is the number of steps that it takes to solve an instance of the problem as a function of the size of the input (usually measured in bits), using the most efficient algorithm.
		The complexity class P is the set of decision problems that can be solved by a deterministic machine in polynomial time.
	en.wikipedia.org /wiki/Computational_complexity_theory (1290 words)

	Complexity classes P and NP - Wikipedia, the free encyclopedia (Site not responding. Last check: 2007-10-09)
		Computational complexity theory is part of the theory of computation dealing with the resources required during computation to solve a given problem.
		Although this particular problem was recently shown to be in P as well (see AKS primality test), this is not at all obvious, and there are many other similar problems that are not believed to be in P.
		All languages in P can be expressed in first-order logic with the addition of a least fixed point operator (effectively, this allows the definition of recursive functions).
	en.wikipedia.org /wiki/Complexity_classes_P_and_NP (2860 words)

	P (complexity) - Psychology Central (Site not responding. Last check: 2007-10-09)
		In computational complexity theory, P is the complexity class containing decision problems which can be solved by a deterministic Turing machine using a polynomial amount of computation time, or polynomial time.
		P is often taken to be the class of computational problems which are "efficiently solvable" or "tractable", although there are potentially larger classes that are also considered tractable such as RP and BPP.
		P is also known to be at least as large as L, the class of problems decidable in a logarithmic amount of memory space.
	psychcentral.com /psypsych/P_(complexity) (700 words)

	Complexity Science
		Complexity science is defined here as an approach to research, study, and perspective which makes the philosophical assumptions of the emerging worldview (EWV) (these include holism, perspectival observation, and others).
		complexity is the study of the behavior of macroscopic collections of such units that are endowed with the potential to evolve in time" (Coveney and Highfield, 1995, p.
		Complexity science opens up a whole new vista of perspectives, approaches, and techniques because it is based on a set of underlying assumptions which differ from classical science.
	polaris.umuc.edu /~edent/emergence/emerge2-r.htm (4223 words)

	Dima Grigoriev: publications (Site not responding. Last check: 2007-10-09)
		Complexity of quantifier elimination in the theory of algebraically closed fields.
		Complexity of quantifier elimination in the theory of ordinary differential equations.
		Complexity of factoring and GCD calculating of ordinary linear differential operators.
	name.math.univ-rennes1.fr /dimitri.grigoriev/articles.html (1697 words)

	The University of Chicago Magazine: December 2002 (Site not responding. Last check: 2007-10-09)
		When Kadanoff refers to the complexity apparent in the delicate ridge of a sand dune or the salt spray coming off a wave, he is conjuring the complicated outcomes that can arise when simple grains of sand or water molecules are placed under certain conditions: high winds, for instance.
		And where physicists are interested in characterizing the unpredictable outcomes of a complex system—the magnitude and direction of a sand-dune avalanche, or the trajectories and sizes of sea-spray droplets—there is a notable absence of chaos in the systems biologists study.
		To study complexity, as Kadanoff has remarked, is to attempt to say something about the “interesting” organization of the world around us, to quantify what seems simple yet defies quantification.
	magazine.uchicago.edu /0212/features (4334 words)

	Complexity Zoo References (Site not responding. Last check: 2007-10-09)
		Primes is in P, Annals of Mathematics, 160 (2004), 781-793.
		On the parameteric complexity of relational database queries and a sharper characterization of W[1], Combinatorics, Complexity, and Logic, Proceedings of DMTCS'96, Springer-Verlag, pp.
		Hilbert's Nullstellensatz is in the polynomial hierarchy, Journal of Complexity 12(4):273-286, 1996, DIMACS TR 96-27.
	www.complexityzoo.com /zooref.html (5760 words)

	Complexity classes P and NP (Site not responding. Last check: 2007-10-09)
		If '''P''' = '''NP''', then all three classes are equal.]] [[Computational complexity theory]] is part of the [[theory of computation]] dealing with the resources required during computation to solve a given problem.
		While this is a common and reasonably accurate assumption in complexity theory, it is not always true in practice, for several reasons:*It ignores constant factors.
		A problem that takes time 10-100002''n'' is not in '''P''' (it is exponential time), but is very tractable for values of ''n'' up into the thousands.*It ignores the size of the exponents.
	complexityclassespandnp.quickseek.com (2038 words)

	Suedfeld's Integrative Complexity References
		Landon, P. B., & Suedfeld, P. Complexity as multidimensional perception: The effects of sensory deprivation on concept identification.
		Suedfeld, P., & Piedrahita, L. Intimations of mortality: Integrative simplification as a precursor of death.
		Suedfeld, P., Lavallee, L., & Brough, J. Political language in an environmental controversy: Integrative complexity and motive imagery in advocacy propaganda and the press.
	www.psych.ubc.ca /~psuedfeld/CXYRefs.html (1366 words)

	Computability and Complexity
		In this section we are dealing with complexity instead of computability, and all the Turing machines that we consider will halt on all their inputs.
		The first important insight in complexity theory is that a good measure of the complexity of an algorithm is its asymptotic worst-case complexity as a function of the size of the input, n.
		Descriptive Complexity: a webpage describing research in Descriptive Complexity which is Computational Complexity from a Logical Point of View (with a diagram showing the World of Computability and Complexity).
	plato.stanford.edu /entries/computability (5266 words)

	Complexity Zoo - Qwiki
		Roughly, the analogue of #P for parameterized complexity.
		In descriptive complexity, uniform AC can be characterized as the class of problems expressible by first-order predicates with addition and multiplication operators - or indeed, with ordering and multiplication, or ordering and division (see [Lee02]).
		If m is a power of a prime p, then for any prime q not equal to p, deciding whether the sum of n bits is congruent to 0 modulo q is not in AC [m] [Raz87] [Smo87].
	qwiki.caltech.edu /wiki/Complexity_Zoo (6334 words)

	'Complexity in Biology' Club at Caltech
		P. Godfrey-Smith, Environmental Complexity and the Evolution of Cognition, in R. Sternberg and J. Kaufman (eds.), The Evolution of Intelligence, Lawrence Erlbaum Associates, 2001
		P. Poirazi and B.W. Mel, Impact of Active Dendrites and Structural Plasticity on the Memory Capacity of Neural Tissue, Neuron 29 (2001), 779-796
		Environmental Complexity and the Evolution of Cognition (Neda Afsarmanesh)
	www.klab.caltech.edu /~ma/cclub (822 words)

	Computational Complexity: What if P = NP?
		P = NP would also have big implications in mathematics.
		One consequence of this is that also the polynomial hierarchy collapses to P. This means that we should be able to solve questions like: "given this list of papers of Erdos, what is the smallest circuit that produced this list".
		A seven million dollar award for showing "P \neq NP" is okay, and it makes sense that we would have an easier and more efficient life assuming P=NP.
	weblog.fortnow.com /2004/05/what-if-p-np.html (954 words)

	Wikinfo \| Complexity classes P and NP (Site not responding. Last check: 2007-10-09)
		The intersection of P and NPC equals the empty set.
		is not P (in fact, it's exponential time), but is very tractable for values of n up into the thousands.
		Images, some of which are used under the doctrine of Fair use or used with permission, may not be available.
	www.wikinfo.org /wiki.php?title=Complexity_classes_P_and_NP (1539 words)

	PRIMES is in P little FAQ (Site not responding. Last check: 2007-10-09)
		Complexity theory is a field in theoretical computer science which attempts to quantify the difficulty of computational tasks and tends to aim at generality while doing so.
		"Complexity" is measured by various natural computing resources, such as the amount of memory needed, communication bandwidth, time of execution, etc. By analyzing several candidate algorithms for a problem, a most efficient one can be easily identified.
		What is P? P stands for a class of decisional problems (problems for which you can answer "yes" or "no") for which any instance of the problem can be solved by a deterministic algorithm in time that can be bounded by a polynomial on the size of the input of the problem.
	crypto.cs.mcgill.ca /~stiglic/PRIMES_P_FAQ.html (2589 words)

	Computability and Complexity (Site not responding. Last check: 2007-10-09)
		The Space Complexity of a decision problem, f, is the amount of memory used by the `best' algorithm A for f.
		A major open problem in Computational Complexity Theory is to develop arguments by which important computational problems can have their time complexity described exactly.
		P is the class of problems with efficient `finding' algorithms.
	www.csc.liv.ac.uk /~ped/teachadmin/algor/comput_complete.html (5669 words)

	Complexity & Chaos in Economic Geography
		Complexity : hierarchical structures and scaling in physics.
		Complex landscapes of spatial interaction; [Abstract & pfd full text] Annals of Regional Science, Volume 35 Issue 1 (2001) pp 81-111.
		Rosser, J. Barkley Jr., "On the Complexities of Complex Economic Dynamics, "Journal of Economic Perspectives, 13(4), Fall 1999, 169-192.
	faculty.washington.edu /~krumme/readings/complexity.html (536 words)

	Kolmogorov Complexity and Solomonoff Induction
		To be brief, K is an excellent universal complexity measure, suitable e.g.
		The major drawback of K as complexity measure is its incomputability.
		A gentle tour of Kolmogorov complexity and its applications, presented by Chris Hillman at UIUC, April 1999, in PostScript.
	www.idsia.ch /~marcus/kolmo.htm (1308 words)

	Computational Complexity: P/poly
		It combines time and program-size complexity, and characterizes non-uniform efficient time and languages with small circuit complexity.
		Some argue that P/poly is a better notion of efficient computation than P since we allow the program size as well as the time to grow as the input grows.
		A better name for P/poly might be "non-uniform P" (maybe a notation P/) and we should reserve the awkward P/f(n) notation for cases when f(n) is a proper sub-class of polynomials.
	weblog.fortnow.com /2005/09/ppoly.html (585 words)

	Complexity Digest - Networking the Complexity Community
		Excerpts: In complex biological systems, entities that are conceptually distinct but empirically related - such as sunlight and plant growth or antigene and immune response - are being explicitly linked through the identification of highly specific uninterrupted interaction sequences that take place between their macromolecular system components.
		Excerpts: As the financial markets increasingly move into the realm of computer models and derivative instruments, the ramifications for the global economy and the lives we lead are only beginning to be understood.
		Our study suggests the existence of more complex patterns of intraspecific diversity than was previously recognized.
	www.comdig.com /index.php (6600 words)

	Complex Systems, Neutral Networks, etc.
		Crutchfield, J.P., van Nimwegen, E. The Evolutionary Unfolding of Complexity (adap-org/9903001).
		P., (1993) Revisiting the Edge of Chaos: Evolving Cellular Automata to Perform Computations Complex Systems 7, 89--130, 1993.
		Seth, A.K., (1998) The Evolution of Complexity and the Value of Variability In Proceedings of the 6th International Conference on Artificial Life (ALIFE VI), eds.
	www.cogs.susx.ac.uk /users/ezequiel/alife-page/complexity.html (1839 words)

	Bibliography "The Evolution of Complexity" (Site not responding. Last check: 2007-10-09)
		The people who submitted abstracts for the Symposium "The Evolution of Complexity" : Evolutionary and cybernetic foundations for transdisciplinary integration" were asked to include references to the literature.
		This is a good popular overview of the development of ideas that was at the basis of the Santa Fe Institute for the sciences of complexity.
		Favati P. Lotti, and L. Margara, Additive Monodimensional Cellular Automata are Chaotic According to the Devaney's Definition of Chaos.Submitted for Publication, 1994.
	pespmc1.vub.ac.be /evocobib.html (3539 words)

	C A P: Complexity Adaptive Processing
		Energy Efficient Co-Adaptive Instruction Fetch and Issue, A. Buyuktosunoglu, T. Karkhanis, D.H. Albonesi, and P. Bose, 30th International Symposium on Computer Architecture, pp.
		Reducing the Complexity of the Register File in Dynamic Superscalar Processors, R. Balasubramonian, S. Dwarkadas, and D.H. Albonesi, 34th International Symposium on Microarchitecture, pp.
		Mechanism for Dynamically Adapting the Complexity of a Microprocessor, D.H. Albonesi, U.S. Patent 6,205,537, issued March 20, 2001.
	www.ccs.rochester.edu /projects/cap/cappublications.htm (1524 words)

	COS 522: Computational Complexity Theory: Home Page
		Complexity classes associated with these models: NP, Polynomial hierarchy, BPP, P/poly, etc. Complete problems.
		After that the topics will often be a little different.
		Expander walk extractors and their use in Nisan's prg for logspace computation.
	www.cs.princeton.edu /courses/archive/spring03/cs522 (184 words)

	DBLP: Salil P. Vadhan
		Boaz Barak, Shien Jin Ong, Salil P. Vadhan: Derandomization in Cryptography.
		Ran Raz, Omer Reingold, Salil P. Vadhan: Extracting all the Randomness and Reducing the Error in Trevisan's Extractors.
		Oded Goldreich, Salil P. Vadhan, Avi Wigderson: Simplified derandomization of BPP using a hitting set generator.
	informatik.uni-trier.de /~ley/db/indices/a-tree/v/Vadhan:Salil_P=.html (1251 words)

	BEATCS Computational Complexity Column
		Please contact the editor if you have any comments on the column or suggestions for future column topics.
		Number 52, February, 1994, The Role of Relativization in complexity theory
		by Richard Chang and P. Rohatgi, in Current Trends in Theoretical Computer Science, G. Rozenberg and A. Salomaa, ed., World Scientific Series in Computer Science, Vol.
	theorie.informatik.uni-ulm.de /Personen/toran/beatcs (834 words)

	LSE Complexity Bibliography
		Allen P. (1998), ‘Complexity, Organisation and Knowledge: The Law of Excess Variety’, in Mitleton-Kelly (1998), 7-29
		Byrne D. Complexity Theory and the Social Sciences: An Introduction.
		McKelvey B. ‘Self-organization, Complexity, Catastrophe, and Microstate Models at the Edge of Chaos’, in Baum and McKelvey (1999), 279-307
	www.psych.lse.ac.uk /complexity/bibliography.htm (6663 words)

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