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Topic: Complete (complexity)

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	Completeness - Wikipedia, the free encyclopedia
		It should be noted that "complete" here is just a term that takes on specific meanings in specific situations, and not every situation in which a type of "completion" occurs is called a "completion".
		Furthermore, an ordered field is complete if every non-empty subset of it that has an upper bound within the field has a least upper bound within the field, which should be compared to the (slightly different) order-theoretical notion of bounded completeness.
		In computational complexity theory, a problem P is complete for a complexity class C, under a given type of reduction, if P is in C, and every problem in C reduces to P using that reduction.
	en.wikipedia.org /wiki/Complete (689 words)

	What is complexity?
		Complexity can only exist if both aspects are present: neither perfect disorder (which can be described statistically through the law of large numbers), nor perfect order (which can be described by traditional deterministic methods) are complex.
		Complexity can then be characterized by lack of symmetry or "symmetry breaking", by the fact that no part or aspect of a complex entitity can provide sufficient information to actually or statistically predict the properties of the others parts.
		The complexity produced by differentiation and integration in the spatial dimension may be called "structural", in the temporal dimension "functional", in the spatial scale dimension "structural hierarchical", and in the temporal scale dimension "functional hierarchical".
	pespmc1.vub.ac.be /COMPLEXI.html (1887 words)

	P-complete - Wikipedia, the free encyclopedia
		In complexity theory, the complexity class P-complete is a set of decision problems and is useful in the analysis of which problems can be efficiently solved on parallel computers.
		A decision problem is in P-complete if it is complete for P, meaning that it is in P, and that every problem in P can be reduced to it in polylogarithmic time on a parallel computer with a polynomial number of processors.
		In other words, a problem A is in P-complete if, for each problem B in P, there are constants c and k such that B can be reduced to A in time O((log n)
	en.wikipedia.org /wiki/P-complete (878 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)

	Circuit Complexity
		The circuit complexity of a binary function is measured by the size or depth of the smallest or shallowest circuit for it.
		Circuit complexity derives its importance from the corollary to Theorem
		Unfortunately, it is generally much more difficult to derive good lower bounds on circuit complexity than good upper bounds; an upper bound measures the size or depth of a particular circuit whereas a lower bound must rule out a smaller size or depth for all circuits.
	www.cs.brown.edu /~jes/book/BOOK/node16.html (381 words)

	JYI: The Limits of Computation (Site not responding. Last check: 2007-11-03)
		Computational complexity — one of the oldest branches of computer science — provides a theory on what is not possible (or feasible) for computers to compute.
		Recall that the complexity of an algorithm is expressed in terms of the size of its input.
		The complexity class P is defined to be the set of decision problems for which there exists a polynomial-time algorithm.
	www.jyi.org /volumes/volume10/issue2/articles/widjaja.html (4848 words)

	Complete Problems
		If the complexity of one complete problem is known, that of all complete problems is known.
		A problem Q is complete for C under R-reduction if it is hard for C under R-reductions and is a member of C. Problems are hard for a class if they are as hard to solve as any other problem in the class.
		Complete problems are members of the class for which they are hard.
	www.geocities.com /s2swen/song.html (1657 words)

	[No title]
		Complexity by definition is something consisting of several parts, or that is in some way complicated.
		Big O notation is simply a way of expressing the algorithms complexity, in terms of rate of growth of the time taken to complete the most complex part of the algorithm.
		When the complexity of an algorithm becomes so great that it is intractable, then in order to solve the problem it would take more time than is realistic to spend finding a solution.
	goanna.cs.rmit.edu.au /~linpa/258/goodpapers/modrich.html (1606 words)

	The Growth of Complexity
		The question of why complexity of individual systems appears to increase so strongly during evolution can be easily answered by combining the traditional cybernetic idea of the "Law of Requisite Variety" and a concept of coevolution, as used in the evolutionary "Red Queen Principle".
		Ashby's Law of Requisite Variety states that in order to achieve complete control, the variety of actions a control system should be able to execute must be at least as great as the variety of environmental perturbations that need to be compensated.
		The present argument does not imply that all evolutionary systems will increase in complexity: those (like viruses, snails or mosses) that have reached a good trade-off point and are not confronted by an environment putting more complex demands on them will maintain their present level of complexity.
	pespmc1.vub.ac.be /COMPGROW.html (1404 words)

	THEORY CANAL: The Rochester Theory Seminar Series
		It is desirable to have easily applied tools (theorems, classification tests, complete characterizations, etc.) that in one fell swoop classify a large class of problems in the domain of interest.
		We study the complexity of two elementary problems in linear algebra, the matrix rank and the determinant, with respect to their approximability using enumerators.
		These results shed some light on the complexity of elementary linear algebra problems that are equivalent to either the rank or the determinant.
	www.cs.rochester.edu /u/www/u/lane/=seminar-theorycanal/seminar-2003-2004.html (1816 words)

	Stas Busygin's NP-Completeness Page
		A problem of a class is complete if you can solve any other problem of this class in polynomial time having a polynomial time algorithm for the first one.
		Hence complete problems are hardest in their own classes and as they exist we may choose any of them to advance solving techniques for the entire class.
		The concept of complete problems for a class is generalized to hard problems for the class by inclusion of all other problems, whose polynomial time algorithm gives polynomial time solvability for the class.
	www.busygin.dp.ua /npc.html (896 words)

	Average-Case Complexity Forum (Site not responding. Last check: 2007-11-03)
		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)

	Complexity Theory
		The time complexity of an algorithm is one of the most common determinants of the success of a computational strategy, although occasionally one finds that exorbitant amounts of energy or incredible numbers of particles can be substituted for a long amount of time.
		Determining the complexity class of a program is difficult because of the negative nature of this definition: one must show that no one can make a faster program.
		Finally, circuit size/depth complexity can be defined for a language as the size/depth complexity of a minimal circuit family for that language.
	www.media.mit.edu /physics/pedagogy/babbage/texts/ct.html (2297 words)

	NP-Completeness and Origami
		NP-complete problems are defined by their computational complexity, which measures how the work involved in solving a problem relates to the size of the problem itself.
		You do this n times and thus the problem’s complexity is said to be of order n, abbreviated as O(n).
		The complexity arises when edges and layers start to collide in a large pattern.
	pr.caltech.edu /periodicals/EandS/articles/LXVII1/NPcompleteness.html (844 words)

	Complexity Digest - Power-Laws In The Complete Sequences Of Human Genome
		Power-Laws In The Complete Sequences Of Human Genome, J.
		Excerpt: The distance distributions of the four types of bases A, C, G and T in the complete sequences of human genome are shown to have long-tail power-law but short-distance exponential behaviors.
		The DNA sequence of E. coli, which is much shorter than human's, is shown to exhibit essentially exponential behavior as its corresponding random sequence.
	www.comdig.org /article.php?id_article=21624 (138 words)

	Complexity Zoo - Qwiki
		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]).
		DistNP has complete problems [Gur87], although unlike for NP this is not immediate.
		There exists a problem that is complete for E under polynomial-time Turing reductions but not polynomial-time truth-table reductions [Wat87].
	qwiki.caltech.edu /wiki/Complexity_Zoo (6395 words)

	Reliable Identification of Bounded-length Viruses is NP-complete
		The question of whether complexity theory is on the side of virus writers or the protection vendors could have important practical implications.
		In this paper we will prove that there exist realistic viruses whose reliable detection is of NP-complete complexity [1] and that therefore the general problem of reliable bounded-length virus identification is NP-complete.
		The complexity of detecting a known fixed virus pattern of length M in a program of length N is harnessed by the Boyer-Moore string-searching algorithm [16] which never uses more than N+M steps and under many circumstances (a small pattern and a large alphabet) can use about N/M steps.
	www.spinellis.gr /pubs/jrnl/2002-ieeetit-npvirus/html/npvirus.html (2705 words)

	Computability and Complexity
		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.
		Kurt Gödel, 1930, "The Completeness of the Axioms of the Functional Calculus," in (van Heijenoort, 1967), 582-591.
		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 (5283 words)

	[No title] (Site not responding. Last check: 2007-11-03)
		Scope, Complexity, and % Complete: scope should be a brief scope definition of the Project status being reported on.
		Estimate at Completion (EAC): This is a forecasted estimate of the total cost of the project based upon the current project schedule, the estimated task durations, staffing levels, and other assumed costs and expenditures.
		Funding Source Summary Section: should be completed to indicate how the project is funded, if there is a percentage spread of funding, the approved funding sources start and end dates, the approved dollar value based on percentage, dollar value remaining, and whether an amendment is in process.
	www.dhs.state.or.us /admin/pmo/data/controlling_templates/status_report_template.doc (1480 words)

	[No title]
		It is an exercise that has the participant(s) rate 7-8 business complexity attributes and technical complexity attributes on a scale from one to five.
		These rating are used to determine a business complexity and technical complexity trend to guide the amount of project management planning and controls and to obtain a Rough Order of Magnitude (ROM) of project costs, duration, and FTE’s..
		It may also be appropriate to complete a complexity analysis trend and ROM for each phase of the project.
	www.oregon.gov /DAS/IRMD/CIO/docs/DHS_business_and_technical_complexity_assessment.doc (1497 words)

	Programming Tools: Code Complexity Metrics \| Linux Journal
		I define complexity of code as the amount of effort needed to understand and modify the code correctly.
		where M is the McCabe Cyclomatic Complexity (MCC) metric, E is the number of edges in the graph of the program, N is the number of nodes or decision points in the graph of the program and X is the number of exits from the program.
		(2) McCabe's complexity is at least as well established as function points, at least among those who know enough of the literature to understand the difference between a volume and a complexity measure.
	www.linuxjournal.com /article/8035 (1330 words)

	Separating Complexity Classes Using Structural Properties
		We study the robustness of complete sets for various complexity classes.
		A complete set A is robust if for any f(n)-dense set S ∊ P, A - S is still complete, where f(n) ranges from log(n), polynomial, to subexponential.
		We show that robustness can be used to separate complexity classes: for every \le _m^p-complete set A for EXP and any subexponential dense sets S ∊ P, A - S is still Turing complete and under a reasonable hardness assumption even \le _m^p-complete.
	csdl2.computer.org /persagen/DLAbsToc.jsp?resourcePath=/dl/proceedings/&toc=comp/proceedings/ccc/2004/2120/00/2120toc.xml&DOI=10.1109/CCC.2004.1313820 (238 words)

	Complexity Theory Lecture Notes (summaries) (Site not responding. Last check: 2007-11-03)
		We define ``nice'' complexity bounds; these are bounds which can be computed within the resources they supposedly bound (e.g., we focus on time-constructible and space-constructible bounds).
		We define space complexity using an adequate model of computation in which one is not allowed to use the area occupied by the input for computation.
		Then we study the complexity class NL (the set of languages decidable within Non-Deterministic Logarithmic Space): We show that directed graph connectivity is complete for NL.
	eccc.hpi-web.de /eccc-local/ECCC-LectureNotes/IntroComplTh/cc-sum.html (2064 words)

	Proof Complexity
		Proof complexity is the study of the lengths of easily-verifiable proofs for co-NP languages.
		The classifications given by proof complexity and lower bounds on the sizes of these proofs permit us to show that large classes of deterministic algorithms require exponential time to solve the problems.
		For example, we have developed new proof systems, based on a result from algebra known as Hilbert's Nullstellensatz, that both extend the range of cases for which we have efficient proofs and have the property that finding a proof is not substantially more difficult than writing it down.
	www.cs.washington.edu /homes/beame/projects/proofcomplexity.html (756 words)

	Computational Complexity (Site not responding. Last check: 2007-11-03)
		The time complexity, or the running time of the algorithm, is the "time" needed by the algorithm (e.g., number of elementary operations such as additions and comparisons) expressed as a function of the problem size.
		It may not find the optimal solution, but it is a good heuristic algorithm with a time complexity of O(n log n); order (n log n) being the complexity of sorting n numbers in descending order.
		Therefore, for the purposes of computational complexity, it is sufficient to be concerned with the recognition problems.
	benli.bcc.bilkent.edu.tr /~omer/research/complexity.html (1766 words)

	Computational Complexity: Favorite Theorems: Combinatorial NP-Complete Problems
		Computational complexity and other fun stuff in math and computer science as viewed by Lance Fortnow.
		I am always happy to hear your ideas, comments and questions about computational complexity and this weblog.
		In this paper we give theorems which strongly suggest, but do not imply, that these problems, as well as many others, will remain intractable perpetually.
	weblog.fortnow.com /2005/05/favorite-theorems-combinatorial-np.html (382 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.
		So before explain the basic ideas of the parallel complexity, we review the basic notions of the classical complexity theory, so that we can understand how the parallel complexity theory relates to the classical one.
		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)

	Computer Laboratory - Computer Science Syllabus - Complexity Theory
		The aim of the course is to introduce the theory of computational complexity.
		The course will explain measures of the complexity of problems and of algorithms, based on time and space used on abstract models.
		Important complexity classes will be defined, and the notion of completeness established through a thorough study of NP-completeness.
	www.cl.cam.ac.uk /DeptInfo/CST/node49.html (171 words)

	Sets of Low Information Content
		Particular emphasis is given to the question of whether sparse sets can be complete for the fundamental complexity classes, such as NP, via the standard types of reductions.
		The above-mentioned studies motivated researchers to study more broadly the classes of sets whose complete languages could not be reduced to sparse sets unless the classes collapsed, and this is a central focus of this project.
		Another motivation for the study of sparse sets is their close relationship to notions of polynomial-time ``quasi-solvability.'' The class of sets having polynomial-size circuits is exactly the class of sets that are polynomial-time Turing reducible to sparse sets (this is due to A. Meyer).
	www.cs.rochester.edu /users/faculty/lane/low-information-sets.html (830 words)

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