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Topic: Complexity theory

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Complexity classes P and NP

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	Computational complexity theory - Wikipedia, the free encyclopedia
		Complexity theory is part of the theory of computation dealing with the resources required during computation to solve a given problem.
		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.
	en.wikipedia.org /wiki/Computational_complexity_theory (1129 words)

	Kids.net.au - Encyclopedia Computational complexity theory -
		The time complexity of a problem is the number of steps that it takes to solve an instance, as a function of the size of the instance.
		The following are some of the classes of problems considered in complexity theory, along with rough definitions.
		In computing the complexity of an algorithm is a formal notion to describe its "speed".
	www.kids.net.au /encyclopedia-wiki/co/Computational_complexity_theory (965 words)

	COMPLEXITY THEORY AND MANAGEMENT PRACTICE by JONATHAN ROSENHEAD
		Given that the key finding claimed for complexity theory is the effective unknowability of the future, the common assumption among managers that part of their job is to decide where the organisation is going, and to take decisions designed to get it there is seen as a dangerous delusion.
		Krugman (1996), on the concluding page of his exploration of the relevance of complexity theory for economics, states "at this point I have no recommendations to offer." By contrast in the management complexity literature there is a tendency to make just such unwarranted statements – both generalisations and prescriptions.
		So, for example, Huygens developed his wave theory of light with ideas from the familiar view of sound as a wave phenomenon; and Fourier’s theory of heat conduction was constructed by analogy with the known laws of the flows of liquids (Nagel 1961).
	www.human-nature.com /science-as-culture/rosenhead.html (10599 words)

	Complexity Theory - Encyclopedia.WorldSearch (Site not responding. Last check: 2007-09-06)
		Computational complexity theory: a field in theoretical computer science and mathematics dealing with the resources required during computation to solve a given problem
		Complexity theory is sometimes used as a broad term addressing the study of complex systems, including subjects such as chaos theory, artificial life, genetic algorithms, and the topics studied by the Santa Fe Institute http://www.santafe.edu
		The authors present the theory in a concise and straightforward manner, with an eye out for the practical applications.
	encyclopedia.worldsearch.com /complexity_theory.htm (277 words)

	Simple, Yet Complex - Business Management - CIO Enterprise Magazine April 15, 1998 (Site not responding. Last check: 2007-09-06)
		Complexity theorists argue that managers should allow creativity and efficiency to emerge naturally within organizations rather than imposing their own solutions on their employees.
		Complexity theory looks at these systems in ways that are organic, nonlinear and holistic.
		A complexity theory perspective is particularly helpful to disheartened, disconnected companies where workers lack commitment--rather, they just watch the clock and work to pick up a pay check.
	www.cio.com /archive/enterprise/041598_qanda_content.html (2489 words)

	Complexity (Site not responding. Last check: 2007-09-06)
		Complexity is a measure of variety of states in the system.
		Complexity is being marked by an involvement of many parts, aspects, details, notions, and necessitating earnest study or examination to understand or cope with (Webster's Third International Dictionary; Klir, 1985).
		Complexity is a perceived systems attribute which increases as the number and variety of elements and relationships within the system becomes greater, and increases as the level of predictability and understanding of the system as a whole decreases (McCarthy, 1995)."
	complexity.martinsewell.com (311 words)

	Complexity Theory (Site not responding. Last check: 2007-09-06)
		Complexity is not a tool, but a way of thinking--a mental model for considering problems in new and revealing ways.
		Complexity applied to knowledge management by a veteran consultant who has seen a lot and knows a lot.
		A compelling historical account of the limitations of Newtonian science and the dynamics of complexity by a Nobel laureate in chemistry, with an emphasis on thermodynamics and dissipative structures.
	www.petzinger.com /complexity.shtml (933 words)

	The Evolving Essence of the Science of Nursing, A Complexity Integration Nursing Theory
		Both theorists recognized the placement of the components between each of the theories and the complexity integration of the chief components of the two theories as significant and essential for the advancement of professional nursing on a global perspective.
		Therefore, the complexity integration of the two nursing theories demonstrates an evolutionary pathway for introducing a paradigm shift in the essence of the science of nursing necessary for the acceptance, implementation, and evaluation of the global concept of “Health for All”.
		A New Nursing Theory is born in Greece.
	www.nursing.gr /theory (1835 words)

	Complexity & Information Theory
		Many alternative mathematical frameworks exist for quantifying the notions of complexity or information, including the algorithmic information theory discussed here, the classical information theory of Shannon and Weaver (1949), logical depth (originally discussed in print by Chaitin 1977; also see Bennett 1982, 1987a, 1990), and others.
		The string's algorithmic information content, or aglorithmic complexity, is bounded from above by the length of the binary sequence specifying 'forty', together with the code which tells the computer to print a digit a certain number of times.
		Another of these short introductory papers explains why, despite the fact that algorithmically complex strings outnumber their simpler cousing by a wide margin, proving that given strings are random is generally impossible.
	www.mulhauser.net /research/tutorials/complexity/complexity.html (1531 words)

	Steve Best-Douglas Kellner: Kevin Kelly's Complexity Theory (Site not responding. Last check: 2007-09-06)
		Drawing on cybernetics, chaos and complexity theory, evolutionary theory, information theory, and discussions of new technologies, Kelly claims that we need fresh models of thought that articulate the parallels between the organization of nature, the novel environments of technology, and the dynamic human and social milieux.
		Like other complex structures such as evolution and life itself, the economy thrives on the "edge of chaos," at the point where it is neither too rigid and static nor unbalanced and amorphous.
		We would distinguish between a conservative and ideological complexity theory that uses new scientific and technological insights in order to legitimate the system of global capitalism, and a critical complexity theory that interprets "bottom-up" power and intelligence in terms of direct democracy, and not a swarmlike hive.
	www.democracynature.org /dn/vol6/best_kellner_kelly.htm (8489 words)

	Complexity (Site not responding. Last check: 2007-09-06)
		Complexity theory attempts to understand some of the surprising and paradoxical consequences which arise when complex systems are operating.
		Organisations are complex systems and complexity theory offers the possibility of helping us understand organisational change and culture rather better than we do at present.
		Chris Langton is one of the pioneers of the cellular automaton approach to complexity.
	www.new-paradigm.co.uk /complexity.htm (854 words)

	Self-Organizing Systems FAQ for Usenet newsgroup comp.theory.self-org-sys
		One measure of complexity is that a complex system comprises multiple levels of description, the more ways of looking at a system then the more complex it is, and more extensive is the description needed to specify it (algorithmic complexity).
		Complexity theory includes some new concepts such as self-organization plus its various specialisms, and adds more prominence to borrowed concepts like emergence, phase space and fitness landscapes, but in essence it relates systems to other systems.
		As K increases, the height of the accessible peaks falls, this is the 'Complexity Catastrophe' and limits the performance towards the mean in the limit.
	www.calresco.org /sos/sosfaq.htm (8398 words)

	Phenomenal Complexity Theory and Change at Disney
		The world of complexity is rich in hetroglossia such that we are always interconnected and a part of it rather than able to be somehow objectively distant from it.
		At issue in complexity theory is the idea that the sum is greater than the parts.
		In terms of phenomenal complexity, Disney is able to able to convince most of its publics that its illusions are the real thing, and that critics are over-zealous or over-reacting.
	cbae.nmsu.edu /~dboje/papers/Disney_phenomenal_complexity.html (3507 words)

	Descriptive Complexity
		Computational complexity was originally defined in terms of the natural entities of time and space, and the term complexity was used to denote the time or space used in the computation.
		This research has settled a major, long standing question in complexity theory by proving the following result: For all s(n) greater than or equal to log n, nondeterministic space s(n) is closed under complementation.
		Logic and Complexity Theory, for the slides of two recent survey talks on descriptive complexity and its applications.
	www.cs.umass.edu /~immerman/descriptive_complexity.html (990 words)

	Social Research Update 18: Complexity Theory and Social Research
		‘Complexity’ is a fundamental challenge to the traditional linear programme in science as a whole and its ideas of certainty and randomness.
		There are three points which need to be made before turning to the implications of complexity theory for the form and content of the social research programme.
		Another way of doing social research in a complexity informed way is to think somewhat differently about the procedures and methods of both quantitative and qualitative social investigation as we are already doing them.
	www.soc.surrey.ac.uk /sru/SRU18.html (2500 words)

	Complexity People (Site not responding. Last check: 2007-09-06)
		Please join us here: mathematicians with interest to Computational Complexity are invited to create their own personal home pages on the World Wide Web or public FTP domains with their on-line accessible papers.
		Our intent is to facilitate the exchange of professional information among the world community of computational complexity.
		In this case a work-around is to either use a different Web-Browser or to view the html-source and follow the links "manually".
	www.eccc.uni-trier.de /eccc/info/people.html (150 words)

	[No title]
		Kolmogorov complexity is a modern notion of randomness dealing with the quantity of information in individual objects; that is, pointwise randomness rather than average randomness as produced by a random source.
		This is impossible by classical probability theory (a branch of measure theory satisfying the so-called Kolmogorov axioms formulated in 1933).
		It is a sharper relative of classical information theory (absolute information of individual object rather than average information over a random ensemble) and yet satisfies many of the laws of classical information theory---although with a slight error term.
	homepages.cwi.nl /~paulv/kolmogorov.html (824 words)

	Complexity Theory Lecture Notes by Oded Goldreich (Site not responding. Last check: 2007-09-06)
		Complexity Theory is a central field of Theoretical Computer Science, with a remarkable list of celebrated achievements as well as a very vibrant present research activity.
		The field is concerned with the study of the intrinsic complexity of computational tasks, and this study tend to aim at generality: It focuses on natural computational resources, and the effect of limiting those on the class of problems that can be solved.
		The course is aimed at exposing the students to the basic results and research directions in the field.
	www.wisdom.weizmann.ac.il /~oded/cc.html (153 words)

	Chaos & Complexity Theory in Education (Site not responding. Last check: 2007-09-06)
		This website is a testbed for ideas that I hope will prove useful to those interested in the intersection of complexity theories and education.
		Complexity theories focus on a way of understanding rather than on a single method or a topic of research or practice.
		It is still unclear just how chaos and complexity theories are best understood and with what range of phenomona they are most useful.
	www.ed.uiuc.edu /chaos (188 words)

	Papadimitriou's home page
		Papadimitriou ``Database metatheory: asking the big queries'' a look at database theory, and CS theory in general, from the point of view of the philosophy/history of science (a one-time experiment), for PODS 95; reprinted in SIGACT News,, Spring 1996.
		Papadimitriou ``Extroverted complexity theory'' a short survey and apologia of work that applies complexity concepts, results, and techniques to fields outside CS.
		On the complexity of pure equilibria, with Alex Fabrikant and Kunal Talwar, explores the complexity of finding pure Nash equilibria in congestion games and similar games, pointing out that many of these problems are PLS-complete (that is, as hard to find as any object whose existence is guranteed by a potential function argument).
	www.cs.berkeley.edu /~christos (1522 words)

	Computational Complexity
		Computational complexity and other fun stuff in math and computer science as viewed by Lance Fortnow.
		descriptive complexity that characterized many common complexity classes in various logics and has connections to the complexity of database queries.
		The greatest gift of computational complexity to society is the ability to use NP-completeness to show that a large variety of problems are likely hard.
	fortnow.com /lance/complog (1796 words)

	Average-Case Complexity Forum (Site not responding. Last check: 2007-09-06)
		Indeed, although NP-complete problems are generally thought of as being computationally intractable, some are easy on average; and some are complete in the average case, indicating that they remain difficult on randomly generated instances.
		This forum provides an overview of the recent research on average complexity, and shows the subtleties in formulating a coherent framework for studying average-case NP-completeness.
		An up-to-date list of research and survey articles in average complexity.
	www.uncg.edu /mat/avg.html (233 words)

	Amazon.com: Books: Complexity: The Emerging Science at the Edge of Order and Chaos (Site not responding. Last check: 2007-09-06)
		Complexity theory most likely will receive other, more rigorous examinations than Waldrop's, but he provides a good grounding of what may indeed be the first flowering of a new science.
		Here, economists work with biologists and physical scientists to develop theories that, many hope, will reveal that while natural systems may operate "at the edge of chaos," they are in fact self-organized.
		This is a book about the science of complexity-a subject that's still so new and so wide-ranging that nobody knows quite how to define it, or even where its boundaries lie.
	www.amazon.com /exec/obidos/tg/detail/-/0671872346?v=glance (1733 words)

	The Complexity and Artificial Life Research Concept for Self-Organizing Systems
		We'll also pursue the wider social implications of these transdisciplinary theories of self-organization on mind, art, spirit and life as it could be...
		Yet everything here is pure science, with lots of art and philosophy thrown in free, reflecting what's striking and best in recent research (our own and that of others) in the new contextual sciences of Complexity Theory plus associated fields.
		CALResCo is a cosmopolitan non-profit organisation dedicated to promoting the wider aspects of the Complex System sciences by education, synthesis and by the integration of the theories into the mainstream viewpoints of arts, philosophy and science.
	www.calresco.org (580 words)

	Column Two: Complexity theory
		Complexity theory is something that seems to keep surfacing in the area of knowledge management, but not as much more than a buzz word.
		Complexity and chaos arose out of dynamical systems.
		Chaos and complexity are nonesense in this case as is all the stuff on patterns seen at all scales.
	www.steptwo.com.au /columntwo/archives/000058.html (253 words)

	Johan Håstad (Site not responding. Last check: 2007-09-06)
		I am an editor for the new open access journal Theory of Computing whose goal is to publish journal papers without commercial publishers taking their cut.
		I am teaching the courses Foundations of cryptography and Theorist's toolkit both during the first half of spring.
		An old set of lecture notes on complexity theory (130 pages).
	www.nada.kth.se /~johanh (201 words)

	Chaos Theory and Complexity Theory
		Although our world is more complex than we can measure, there are underlying patterns that give us understanding and meaning about life.
		You will find a range of resources that will introduce you to this strange and wonderful emerging science, that is heading towards making major changes in how we live our lives.
		glossary of terms used in Chaos and Complexity from the www.calresco.org.
	complexity.orcon.net.nz (255 words)

	Luca Trevisan \| Computational Complexity
		It also looks at the trade-offs and relationships between different "modes" of computation (what if we use randomness, what if we are happy with approximate, rather than exact, solutions, what if we are happy with a program that works only for most possible inputs, rather than being universally correct, and so on).
		In the second part, we will focus on more research oriented material, to be chosen among PCP and hardness of approximation; circuit, proof complexity, and communication lower bounds; and derandomization, average-case complexity and extractors.
		For reasons that are only partially understood, a disproportionate number of the most beautiful results in Complexity theory in the 80s and 90s have been found by Berkeley graduate students.
	www.cs.berkeley.edu /~luca/cs278 (493 words)

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