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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.
		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 (1129 words)

	complex from FOLDOC (Site not responding. Last check: 2007-11-07)
		Complex numbers can be plotted as points on a two-dimensional plane, known as an Argand diagram, where x and y are the Cartesian coordinates.
		An alternative, polar notation, expresses a complex number as (r e^it) where e is the base of natural logarithms, and r and t are real numbers, known as the magnitude and phase.
		Complex numbers are useful in many fields of physics, such as electromagnetism because they are a useful way of representing a magnitude and phase as a single quantity.
	gd.tuwien.ac.at /study/foldoc/foldoc.cgi?complex (602 words)

	Encyclopedia: NP (complexity class)
		In computational complexity theory, NP ("Non-deterministic Polynomial time") is the set of decision problems solvable in polynomial time on a non-deterministic Turing machine.
		Examples are the traveling salesman problem where we want to know if there is a shorter route that goes through all the nodes in a certain network and the satisfiability problem where we want to know if a certain formula in propositional logic with propositional variables is satisfiable or not.
		Whether this is really true or not is still one of the big open questions in computer science (see Complexity classes P and NP for an in-depth discussion).
	www.nationmaster.com /encyclopedia/NP-%28complexity-class%29 (451 words)

	Complexity class -- Facts, Info, and Encyclopedia article (Site not responding. Last check: 2007-11-07)
		In (Click link for more info and facts about computational complexity theory) computational complexity theory, a complexity class is a set of problems of related complexity.
		Some complexity classes are sets of (Click link for more info and facts about function problem) function problems, such as (Click link for more info and facts about FP) FP.
		Many complexity classes can be characterized in terms of the (Any logical system that abstracts the form of statements away from their content in order to establish abstract criteria of consistency and validity) mathematical logic needed to express them; see (Click link for more info and facts about descriptive complexity) descriptive complexity.
	www.absoluteastronomy.com /encyclopedia/c/co/complexity_class.htm (183 words)

	COMPLEXITY CLASS FACTS AND INFORMATION (Site not responding. Last check: 2007-11-07)
		In computational_complexity_theory, a complexity class is a set of problems of related complexity.
		For example, the class NP is the set of decision_problems that can be solved by a non-deterministic_Turing_machine in polynomial_time, while the class PSPACE is the set of decision problems that can be solved by a deterministic_Turing_machine in polynomial_space.
		Many complexity classes can be characterized in terms of the mathematical_logic needed to express them; see descriptive_complexity.
	www.witwib.com /complexity_class (137 words)

	Dieter van Melkebeek - Research on Computational Complexity Theory
		Trying to separate complexity classes by isolating a structural difference between their complete problems, forms a unifying theme in my thesis research.
		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.
		The Kolmogorov complexity of a string is the length of its shortest description; various complexity restrictions on the descriptions lead to various notions of Kolmogorov complexity.
	www.cs.wisc.edu /~dieter/Research/complexity.html (2933 words)

	PlanetMath: complexity class (Site not responding. Last check: 2007-11-07)
		The most common classes are all restricted to one read-only input tape and one output/work tape (and in some cases a one-way, read-only guess tape) and are defined as follows:
		The most important time complexity classes are the polynomial classes:
		This is version 1 of complexity class, born on 2002-09-06.
	planetmath.org /encyclopedia/ComplexityClass.html (210 words)

	Oracle machine - Open Encyclopedia (Site not responding. Last check: 2007-11-07)
		In complexity theory and computability theory, an oracle machine is an abstract machine used to study decision problems.
		The complexity class of decision problems solvable by an algorithm in class A with an oracle for a problem in class B is written A
		For example, the class of problems solvable in polynomial time by a deterministic Turing machine with an oracle for a problem in NP is P
	open-encyclopedia.com /Oracle_(computer_science) (637 words)

	COMPLEXITY (Complexity class of polygon)
		Complexity of soil landscape attribute classes is determined from information provided on source maps and the accompanying soil reports.
		The concept of complexity provides an indication of attribute variability within a polygon, particularly with respect to the classes of parent material deposition modes and soil development.
		Complexity infomation was found in both the DOM and SUBDOM files for any given polygon.
	sis.agr.gc.ca /cansis/nsdb/slc/v2.2/domsub/complexity.html (255 words)

	[No title]
		Bunge defines complexity of an individual to be the “numerosity of its composition”, implying that a complex individual has a large number of properties [Bunge, 1977].
		In the case of objects and classes, the methods and data attributes are the set of properties, and therefore complexity of a class is a function of the interaction between the methods and the data attributes.
		Attribute Complexity (AC) for the class = (R(i) where R(i) is the value of each attribute in the class = (2+2+2+2 + 2+2+2+2) = 16 Therefore the AC of the class = 16.
	itech.fgcu.edu /faculty/rbandi/chap3.doc (1898 words)

	Classes of Problems (Site not responding. Last check: 2007-11-07)
		The complexity classes we have studied are class P, class NP, nonfeasible, and unsolveable.
		If these classes are equal, then all the problems in class NP could be solved in a feasible way.
		These are the complexity class associated with problems that were or will be discussed in class.
	www.cs.uidaho.edu /~karenv/cs213/cs213.useful.pages/classes.html (288 words)

	A Systems View of the EFL Class: Mapping Complexity
		Finally, and significantly in terms of current complexity theories, classical (Newtonian) physics was unable to solve a problem of fundamental interest in physics: the “Many-ball problem” (Brown 1972), in which bodies not interacting in a simple linear fashion could not be described according to the Laws of Motion.
		The educational context, with the classroom at its center, is viewed as a complex system in which events do not occur in linear causal fashion, but in which a multitude of forces interact in complex, self-organizing ways, and create changes and patterns that are part predictable, part unpredictable.
		If the global goal of the language class is communicative competence, then the concept of equifinality states that there are various equally valid ways of achieving that goal, and that the paths taken by self-directed learners (and the learning structures which emerge on the way) might not be predictable at the local level.
	www.eslteachersboard.com /cgi-bin/articles/index.pl?read=909 (3417 words)

	Complexity class Definition / Complexity class Research (Site not responding. Last check: 2007-11-07)
		In computational complexity theoryComplexity 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, r...
		complexity class is a set of problems of related complexity.
	www.elresearch.com /Complexity_class (267 words)

	Complexity (Site not responding. Last check: 2007-11-07)
		Algorithms that are bounded by n to the k-th power, where n is the size of the problem are said to be polynomially complex.
		It is important to recognize that while we have primarily looked at specific algorithms and their complexity, that problems also belong to complexity classes.
		The exponentiation operator is ** and the line labelled 1e10 is the number of microseconds in a day and the line labelled 1e24 is the number of microseconds since the big bang.
	www.cs.uidaho.edu /~karenv/cs101/lectures2/complexity.html (498 words)

	URCS Theory Technical Reports
		We study the complexity of quantum complexity classes such as EQP, BQP, and NQP (quantum analogs of P, BPP, and NP, respectively) using classical complexity classes such as ZPP, WPP, and C_{=}P. The contributions of this paper are threefold.
		Though it is known that, unless surprising complexity class collapses occur, one cannot reduce the number of accepting paths of NP machines [Ogihara and Hemachandra 1993], we nonetheless show that it often is possible to reduce the number of solutions of NP functions.
		It is also shown that all complexity classes of recursive predicates have effective measure zero in the space of recursive predicates and, on the other hand, the class of predicates with almost everywhere complexity above an arbitrary recursive threshold has recursive measure one in the class of recursive predicates.
	www.cs.rochester.edu /trs/theory-trs.html (16004 words)

	Complexity classes
		We have said that complexity classes are concerned with growth, and the tables above have given you some idea of what different behaviour means when it comes to growth.
		There we have chosen a representative each of the complexity classes considered, but we have'nt said anything about just how `representative' such an element is. Let us start with the formal definition of a `big Oh' class.
		Sometimes it is difficult to be sure what the exact complexity is (as is the case with the famous P=NP problem), in which case one might say that an algorithm is `at most', say, quadratic.
	www.cs.bham.ac.uk /~mhe/foundations2/node120.html (422 words)

	Computational Complexity: 09/08/2002 - 09/14/2002 (Site not responding. Last check: 2007-11-07)
		If one insists on a complexity class, one could consider all the languages reducible to FACTOR but there is not much value beyond considering the complexity of the language FACTOR.
		The class UP∩co-UP is arguably the smallest interesting complexity class not known to have efficient algorithms and, assuming factoring is hard, really does not have efficient algorithms.
		On the other hand the hardness of factoring is taken as a given in the study of complexity and cryptography and used to show the hardness of classes like UP∩co-UP.
	weblog.fortnow.com /archive/2002_09_08_archive.html (922 words)

	complexity class (Site not responding. Last check: 2007-11-07)
		complexity class of decision problems for which answers can be checked by an algorithm whose run time is polynomial in the size of the input.
		complexity class of decision problems for which answers can be checked for correctness, given a
		complexity class of decision problems that are intrinsically harder than those that can be solved by a nondeterministic Turing machine in
	www.cs.binghamton.edu /~hzeng/CS552/complexity%20class.htm (796 words)

	Language in India
		Classes are carried out totally in the second language with absolutely no reliance on the first language or on any form of translation.
		In order to keep the level of difficulty and complexity of the passage given for dictation appropriate to the level of students, it is better to select these passages only from the lessons already completed in class.
		The class is lined up and the teacher whispers a message (length and difficulty level appropriate to the class) to the student on the end of the line, who listens and repeats, again in a whisper, to the next student, continuing down the line.
	www.languageinindia.com /april2002/tesolbook.html (20431 words)

	Articles - P (complexity) (Site not responding. Last check: 2007-11-07)
		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.
	www.gaple.com /articles/P_(complexity)?mySession=ff70f147c8c688e41a30ee9797a938be (707 words)

	Complete Problems
		Many complexity classes contain "complete problems," problems that are hardest in the class.
		If the complexity of one complete problem is known, that of all complete problems is known.
		Definition 8.7.3 Let C be a complexity class, R a class of resource-bounded transformations, and P1 and P2 decision problems.
	www.geocities.com /s2swen/song.html (1657 words)

	Computational Complexity: 08/25/2002 - 08/31/2002 (Site not responding. Last check: 2007-11-07)
		Complexity Zoo that gives a short description of many classes that make a good reference.
		Watch this space tomorrow for the first complexity class of the week.
		Feel free to email me with suggestion for future classes of the week, especially if you are willing to contribute a write-up.
	weblog.fortnow.com /archive/2002_08_25_archive.html (796 words)

	Asymptotic complexity (Site not responding. Last check: 2007-11-07)
		The time complexity T(n) is a function of the problem size n.
		The asymptotic complexity is a function f(n) that forms an upper bound for T(n) for large n.
		) is the complexity class of all functions that grow at most quadratically.
	www.iti.fh-flensburg.de /lang/algorithmen/asympen.htm (824 words)

	COMPLEXITY CLASS
		Complexity class A collection of algorithms or computable functions with the same complexity.
		Any of a set of computational problems with the same bounds ((n)) on time and space, for deterministic and nondeterministic machines.
		-5 letters: allotypies, cacomistle, cityscapes, climaxless, collimates, complexity, complicate, cosmically, cytoplasms, ectoplasms, episomally, exotically, mislocates, oscillates, poetically, scapolites, semipostal, smallpoxes, societally.
	www.websters-online-dictionary.org /co/complexity+class.html (222 words)

	PlanetMath: counting complexity class (Site not responding. Last check: 2007-11-07)
		is a complexity class associated with non-deterministic machines then
		is the class of counting problems associated with
		This is version 1 of counting complexity class, born on 2002-09-07.
	planetmath.org /encyclopedia/CountingComplexityClass.html (65 words)

	Computational complexity theory (Site not responding. Last check: 2007-11-07)
		The most common resources are time (how many steps does it take to solve a problem) and space (how much memory does it take to solve a problem).
		However, looking up something in a dictionary has only logarithmic complexity because for a double sized dictionary you have to open it only one time more (e.g.
		Decision problems fall into sets of comparable complexity, called complexity classes.
	www.sciencedaily.com /encyclopedia/computational_complexity_theory (963 words)

	Parallel complexity theory - NC algorithms
		Most of the machinery of the parallel complexity theory is derived from the sequential one, which uses specific formal framework to make its results and conclusions independent on particular implementation details of algorithms and robust with respect to various models and architectures of computing devices.
		Some problems in a class may be easier than the others, but all of them can be solved within the same resource bounds associated with the class.
		Complexity class NP: the class of all languages that can be verified by polynomial-time verification algorithms.
	www.cs.wisc.edu /~tvrdik/3/html/Section3.html (1841 words)

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