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Topic: Computational complexity

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	Introduction to Neural Networks and Computational Complexity
		In general, one speaks of threshold complexity and analog complexity, where the former represents computational complexity on a threshold circuit while the latter considers this on a continuous circuit.
		To simplify, there is in general a computational tradeoff between time and space, and in the case of neural networks this means the tradeoff is between quantity of nodes, quantity of layers, and connectedness of nodes.
		In the neural context one measures the complexity of a function by node complexity, that is, the number of nodes required to compute a given function.
	www.eecs.tufts.edu /~jkroll/neuralcomp.html (4872 words)

	20th WCP: Computational Complexity and Philosophical Dualism
		Of course, one could plausibly argue that the major problems arisen by Complexity Theory, i.e., the size of N (number of steps to solve a problem) and the speed of computing might depend on the type of machine on which the algorithm is to be run.
		Nonetheless, early writings on Complexity Theory by Bremermann (1977) which have been systematically overlooked by many authors (including Penrose) show that there are physical constraints for the design of computing machines and such constraints have a bearing on the time-length consumed by those machines no matter how improved their hardware may be.
		Since the growth of temporal complexity involved in the realization of transcomputable algorithms is exponential that means that the time-length required for running some transcomputable algorithms can be as long as the age of the universe.
	www.bu.edu /wcp/Papers/Cogn/CognTeix.htm (3006 words)

	[No title] (Site not responding. Last check: 2007-11-02)
		Computational complexity itself is related to the least time (or number of steps) needed to carry out a certain computation.
		Thus students of computational complexity are typically concerned with whether a sequence of larger and larger problems can be solved in a time that grows as a polynomial in the size of the problem (rather than an exponential or something worse).
		Most of the effective complexity of the universe lies in the AIC of a description of those frozen accidents and their consequences, while only a small part comes from the simple fundamental laws of the universe, (the law of the elementary particles and the condition at the beginning of the expansion).
	www.santafe.edu /sfi/People/mgm/complexity.html (2458 words)

	Nonlinear Dynamics and Complex Systems Theory (Glossary) (Site not responding. Last check: 2007-11-02)
		The Computational Complexity of a problem is defined as the time it takes for the fastest program running on a universal computer -as measured in number of computing steps, say N -to compute the solution to the problem.
		The Computational Complexity of a problem is then defined as the time it takes for the fastest program running on a universal computer (as measured in number of computing steps) to compute the solution to the problem.
		Computational universality is a property of a certain class of computers such that changes in input alone allow any computable function to be evaluated without any change in internal construction.
	www.cna.org /isaac/Glossb.htm (8566 words)

	Computational Complexity and the Scope of Software Patents
		In short, the use of asymptotic computational complexity to describe not only the efficiency of computer algorithms, but their overall value to the computer science community, is an industry standard.
		By 1965, computer scientists identified as tractable mathematical problems for which a polynomial-time algorithm was known, using asymptotic measures of computational complexity in their analysis.
		Strategically significant computational problems, characterized by the size of the data to be processed and the complexity of the problem to be solved, include molecular modeling, human genome mapping, weather forecasting, pharmaceutical testing, fluid dynamics, signal-image processing, environmental quality modeling, and electronics.
	www.unclaw.com /chin/scholarship/software.htm (5070 words)

	Complexity - Wikipedia, the free encyclopedia
		Computational complexity theory is the study of the complexity of problems - that is, the difficulty of solving them.
		Computational complexity can be investigated on the basis of time, memory or other resources used to solve the problem.
		In computational complexity theory, 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/Complexity (1273 words)

	Natural Selection & Complexity
		When we look at the gamut of increasing complexity that has evolved over geological time and how it has been molded by natural selection, and how it can be put together so that it works mechanically from generation to generation, we cannot avoid a feeling of awe.
		To use a metaphor, the complexity we have in mind is a complexity in the very fabric of the universe.
		That the pattern of physical law should change with scale, that is a complexity inherent in the fabric of the universe, that is a complexity which does not exist in a Newtonian universe.
	asweknowit.ca /evcult/Complexity.shtml (3545 words)

	Computational Complexity Symposium (Site not responding. Last check: 2007-11-02)
		Since past discussions of attention always seem to involve claims of resource limitations, it is natural to look to computational complexity to see if any insights may be gained.
		In particular, we analyze the complexity of computing the Coherence problem when parameterized by c (the number of satisfied constraints) and i (the number of unsatisfied constraints).
		This result presents us with a paradox: Computing a maximally coherent belief system is easy for both low levels and high levels of coherence in belief networks.
	www.ipo.tue.nl /homepages/ivrooij/Symposium_Complexity.htm (778 words)

	Computational complexity theory - Wikipedia, the free encyclopedia
		The most important open question of complexity theory is whether the complexity class P is the same as the complexity class NP, or is merely a subset as is generally believed.
		This is a measure of the size of a boolean circuit needed to compute the answer to a problem, in terms of the number of logic gates required to build the circuit.
		A complexity class is the set of all of the computational problems which can be solved using a certain amount of a certain computational resource.
	en.wikipedia.org /wiki/Computational_complexity_theory (2129 words)

	Complexity Theory
		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.
	www.istheory.yorku.ca /complexitytheory.htm (606 words)

	Complexity Zoo - Qwiki
		Computing the parity or majority of n bits is not in AC There are functions in AC that are pseudorandom for all statistical tests in AC But there are no functions in AC that are pseudorandom for all statistical tests in QP (quasipolynomial time) [LMN93].
		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).
		For each update, it computes a new value for the data structure in FO -- that is, for each bit of the data structure, there is an FO function representing the new value of that bit, which takes as input both the update and the previous value of the data structure.
	qwiki.caltech.edu /wiki/Complexity_Zoo (6771 words)

	Computational Complexity in Physical Processes (Site not responding. Last check: 2007-11-02)
		Theoretical computer science has developed a system for classifying the computational complexity of a wide range of problems, placing them in a hierarchy ranging from simple parallel circuits to PP and NP and on up to undecidable problems such as Turing's Halting Problem.
		These new models of computation are of interest not just because they may lead to new computing technologies (which at this point are admittedly speculative) but because they can help us understand the computational power of continuous and quantum systems just as the current framework of computer science allows us to understand classical, digital systems.
		By building a zoo of examples whose computational complexity is well understood, both in the worst case and on average, they can build intuition about the relationships between computational complexity and dynamics, and, in some cases, develop fast algorithms for systems they care about.
	www.santafe.edu /research/compComplexity.php (1398 words)

	Dieter van Melkebeek - Research on Computational Complexity Theory
		Complexity theory aims to answer this question by describing how many resources we need to compute the solution as a function of the problem size.
		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 (2966 words)

	Computational Complexity
		Computational complexity and other fun stuff in math and computer science as viewed by Lance Fortnow.
		Numb3rs, Charlie the mathematician was seen carrying a copy of the SIAM Journal on Computing, a prominent TCS journal.
		Other computer scientists often complain, rightly or wrongly, that theoretical computer science and computational complexity have lost touch with real computational issues.
	weblog.fortnow.com (1478 words)

	Publications about 'computational complexity'
		This paper investigates computational complexity aspects of a combinatorial problem that arises in the reverse engineering of protein and gene networks, showing relations to an appropriate set multicover problem with large "coverage" factor, and providing a non-trivial analysis of a simple randomized polynomial-time approximation algorithm for the problem.
		Tools from automata theory, logic, and related areas of computer science and finite mathematics are used in the study of PL systems, in conjunction with linear algebra techniques, all in the context of a "PL algebra" formalism.
		The original contribution is in formalizing this comparison in the context of computational complexity.
	www.math.rutgers.edu /~sontag/Keyword/COMPUTATIONAL-COMPLEXITY.html (956 words)

	Complexity Theory page (of Oded Goldreich) (Site not responding. Last check: 2007-11-02)
		In focusing attention on computational tasks and algorithms, computability theory has set the stage for the study of the computational resources (like time) that are required by such algorithms.
		Complexity Theory is a central field of the theoretical foundations of Computer Science.
		That is, a typical Complexity theoretic study looks at a task (or a class of tasks) and at the computational resources required to solve this task, rather than at a specific algorithm or algorithmic scheme.
	www.wisdom.weizmann.ac.il /~oded/cc.html (452 words)

	Computational Complexity
		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.
		Computers are becoming faster and faster with each new generation of chips.
		Therefore, for the purposes of computational complexity, it is sufficient to be concerned with the recognition problems.
	www.csulb.edu /~obenli/Research/IE-encyc/complexity.html (1766 words)

	Computational Complexity Theory (Site not responding. Last check: 2007-11-02)
		A fundamental area of theoretical computer science is complexity theory, the analysis of the resources needed to solve computational problems.
		The research project in Low-Level Complexity conducted by our group attempts to attack such problems by determining the relationships between complexity classes defined in various models by such very severe constraints.
		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.
	www.cs.umass.edu /~immerman/complexity_theory.html (295 words)

	3.3.4 ETAQA-QBD and its Computational Complexity (Site not responding. Last check: 2007-11-02)
		Computation of queue length for the aggregate solution is obtained by computing the sums
		Since the inverse is computed (and stored) in a prior step, we require only two matrix multiplications.
		We emphasize the fact that the sparcity of G is key to preserving the sparcity of the original process in the QBD-aggregate method, while the R that is required in matrix-geometric is usually full.
	www.cs.wm.edu /~riska/main/node38.html (319 words)

	Wiley::Theory of Computational Complexity
		Theory of Computational Complexity offers a thorough presentation of the fundamentals of complexity theory, including NP-completeness theory, the polynomial-time hierarchy, relativization, and the application to cryptography.
		It also examines the theory of nonuniform computational complexity, including the computational models of decision trees and Boolean circuits, and the notion of polynomial-time isomorphism.
		The theory of probabilistic complexity, which studies complexity issues related to randomized computation as well as interactive proof systems and probabilistically checkable proofs, is also covered.
	www.wiley.com /WileyCDA/WileyTitle/productCd-0471345067.html (253 words)

	Computational Complexity (Site not responding. Last check: 2007-11-02)
		The initial purpose of Computational Complexity is to make precise the intuitive idea of a computationally feasible problem.
		The birth of the theory of Computational Complexity can be set in mid 60s when the first users of electronic computers started to pay increasing attention to the performances of their programs.
		The main goals of Computational Complexity theory are to introduce classes of problems that have similar complexity with respect to a specific computation model and to study the intrinsic properties of such classes.
	alpha.fdu.edu /~sharma/images/Computational_Complexity.html (117 words)

	2.9.1 General Computational Complexity (Site not responding. Last check: 2007-11-02)
		One of the most important behavioral aspects of a computation is the complexity of the computation, i.e., the amount of computation resources used during that computation.
		It will play a key role in many of the proofs which follow, so we now define a general notion of computational complexity which is suitable for our generalized model of computability.
		Clearly, the complexity measures defined for LOOP and RAM programs satisfy the first condition of a general computational complexity measre.
	www.cs.pitt.edu /~daley/cs3120/cs3120w_node37.html (407 words)

	Computational Complexity: The H-Number
		From rough and hopelessly inaccurate estimates, if you work in complexity theory then your h-index will be half of an "equivalent" researcher in algorithms, which will be half of an "equivalent" researcher in a more applied community, simply because of the size of the community and the accepted citation patterns.
		In this age of computers there is no real reason to take the base of the publications tower as a proxy for the actual area.
		Such a series of workshops might well resolve a problem that is ripe for tackling such as bringing down the time complexity of Aggarwal's et al.
	weblog.fortnow.com /2006/06/h-number.html (2444 words)

	ICC'01 - Implicit Computational Complexity
		Several machine-independent approaches to computational complexity have been developed, which characterize complexity classes by conceptual measures borrowed primarily from mathematical logic.
		Practically, implicit computational complexity provides a framework for a streamlined incorporationof computational complexity into areas such as formal methods in software development, programming language theory.
		In addition to research reports on theoretical advances in implicit computational complexity, practical contributions bridging the gap between Computational Complexity and Programming Language Theory are therefore of particular interest.
	www.dcs.ed.ac.uk /home/mxh/ICC01.html (274 words)

	Computational Complexity Conference Call for Papers (Site not responding. Last check: 2007-11-02)
		We also encourage results from other areas of computer science and mathematics motivated by topics in complexity theory.
		The conference is sponsored by the IEEE Computer Society Technical Committee for Mathematical Foundations of Computing in cooperation with ACM SIGACT and EATCS.
		This year the conference is one of the constituent conferences of the Federated Computing Research Conference (FCRC 2007).
	facweb.cs.depaul.edu /jrogers/complexity/cfp.htm (678 words)

	Workshop on Implicit Computational Complexity
		It aims at studying the computational complexity of programs without refering to a particular machine model and explicit bounds on time or memory, but instead by relying on logical or computational principles that entail complexity properties.
		We propose a new complexity measure of space for the BSS model of computation.
		One of the approaches to Implicit Computational Complexity consists in using the resource limitations built in Girard's Linear Logic to design type theories which enforce complexity constraints on underlying lambda-terms and which are expressive enough to exhaust the respective complexity classes.
	www-lipn.univ-paris13.fr /~baillot/GEOCAL06/ICCworkshop.html (2588 words)

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