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Topic: Computation problem

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	Decision problem Summary
		In this sense, a decision problem is equivalent to a formal language.
		Nearly every problem can be cast as a decision problem by using reductions, often with little effect on the amount of time or space needed to solve the problem.
		In computational complexity, decision problems which are complete are used to characterize complexity classes of decision problems.
	www.bookrags.com /Decision_problem (1398 words)

	Computation and Biology
		The computation is simplified dramatically by (1) approximating the multi-dimensional joint probabilities of all the data by the product of marginal probabilities (hence the name pseudo-likelihood), (2) exploiting the special properties of transition matrix and (3) using a hidden Markov chain algorithm.
		This is because the computational requirement for simulating samples increases exponentially with the selection rate and also due to needing to simulate a sample of size one from the population at equilibrium.
		Computations indicate that the genome organization of wild-type T7 is nearly optimal for growth: only 2.8% of random genome permutations were computed to grow faster, the highest 31% faster, than wild type.
	lansbury.bwh.harvard.edu /computation_biology.htm (14717 words)

	On Protocol Security in the Cryptographic Model
		This in particular becomes a problem when the party that you do not trust is one which is separated from you and is one on which you depend, e.g.
		The usual way of formalizing the problem is to say that a number of parties who do not trust each other wish to compute some function of their local inputs, while keeping their inputs as secret as possible and guaranteeing the correctness of the output.
		A general solution to the secure multiparty computation problem is a compiler which given any feasible function describes an efficient protocol which allows the parties to compute the function securely on their local inputs over an open network.
	www.brics.dk /DS/03/8 (716 words)

	Teaching Math Computation and Problem Solving Skills
		They also begin to solve word problems in which the numbers are vertically aligned, but blank spaces are provided after the numbers for students to write the name of the manipulative object used in the lesson.
		Students continue to solve word problems in which the numbers are vertically aligned, but now they fill in the blanks with the name of the representational drawing rather than the manipulative objects used in earlier lessons.
		Students frequently become passive when faced with problems they perceive to be difficult (i.e., they tend to guess, depend on the teacher or peers for the answer, or quit working altogether).
	deafed.department.tcnj.edu /math/computation.html (1540 words)

	Computation problem - Wikipedia, the free encyclopedia
		In computability theory a computation problem is determining whether or not there exists a computation procedure or algorithm for a class S of questions requiring a non-Boolean value (i.e., a value from {1, 2, 3...}).
		These are also known as what-questions and differ from the class of questions requiring a Boolean value (see decision problem).
		The class of functions that are computable is countably infinite whereas the class of all functions is uncountable.
	en.wikipedia.org /wiki/Computation_problem (149 words)

	Function problem - Wikipedia, the free encyclopedia
		In computational complexity theory, a function problem is a problem other than a decision problem, that is, a problem requiring a more complex answer than just YES or NO.
		Function problems are more awkward to study than decision problems because they don't have an obvious analogue in terms of languages, and because the notion of reduction between problems is more subtle as you have to transform the output as well as the input.
		This places the traveling salesman problem in the complexity class FP (the class of function problems which can be solved in polynomial time on a deterministic Turing machine with an oracle for a problem in NP), and in fact it is complete for that class.
	en.wikipedia.org /wiki/Function_problem (345 words)

	Open Algorithmic Problems
		quadratic lower bounds for the colinear points problem in several (slightly) different models of computation, but the minimum-area triangle problem cannot even be solved in the models in which my lower bounds hold.
		I have established a quadratic lower bound for the real problem, but the complex problem cannot even be solved in the models in which my lower bound holds.
		The problem is open even in the special case where the lines form two pencils, and the source and target points are corners of the distorted grid they form.
	compgeom.cs.uiuc.edu /~jeffe/open/algo.html (698 words)

	Lagally Research Group
		After the computation is completed, the code of the remaining DNA is deciphered to reveal the solution to the problem.
		Because of the ability to perform biochemical operations simultaneously on many different DNA molecules, a problem that would take all the supercomputers in the world running in parallel years to solve could, in principle, be solved in a matter of minutes with a DNA computer.
		In DNA computation, difficult computation problems deemed intractable are investigated using the parallel approach of DNA.
	mrgcvd.engr.wisc.edu /lagallygroup/research/DNA/DNA_Computation.htm (1052 words)

	Quantum Computing (Stanford Encyclopedia of Philosophy)
		The cost of computing a function is also of great importance, and this cost, also known as computational complexity, is measured naturally in the physical resources (e.g., time, space, energy) invested in order to solve the computational problem at hand.
		Computer scientists classify computational problems according to the way their cost function behaves as a function of their input size, n, (the number of bits required to store the input) and in particular, whether it increases exponentially or polynomially with n.
		The problem is that while some prototypes of the simplest elements needed to build a quantum computer have already been implemented in the laboratory, it is still an open question how to combine these elements into scalable systems.
	plato.stanford.edu /entries/qt-quantcomp (9666 words)

	Secure Multiparty Computation for Privacy Preserving Data Mining
		This problem is actually a special case of a long-studied problem in cryptography: secure multiparty computation.
		The aim of a secure multiparty computation task is for the participating parties to securely compute some function of their distributed and private inputs.
		(For example, a decision tree computed on two distributed databases reveals some information about both databases.) Therefore, the privacy requirement is usually formalized by saying that the only information learned by the parties in the computation (again, even by those who behave maliciously) is that specified by the function output.
	www.cs.biu.ac.il /~lindell/research-statements/mpc-ppdm.htm (3319 words)

	2.2 Partitioning
		A focus on the computations that are to be performed can sometimes reveal structure in a problem, and hence opportunities for optimization, that would not be obvious from a study of data alone.
		Arrows represent exchanges of data between components during computation: the atmosphere model generates wind velocity data that are used by the ocean model, the ocean model generates sea surface temperature data that are used by the atmosphere model, and so on.
		Particularly in science and engineering applications, where the problem to be solved may involve a simulation of a complex physical process, the approximations and numerical techniques used to develop the simulation can strongly influence the ease of parallel implementation.
	www-unix.mcs.anl.gov /dbpp/text/node16.html (1503 words)

	COMP 205: Official Syllabus (UNC-CH Computer Science)
		Thus it should involve solving a real scientific problem, should require the solution of a range of numerical problems, and should involve the student in programming solutions to real parts of the problem, experiencing the speeds and accuracies that result from the choice of methods.
		Problems of inconsistency in geometric computations by using line-intersection problems.
		Lecture 8: Problems in computing convex hull in 3D due to finite precision arithmetic and degenerate data.
	www.cs.unc.edu /Admin/Courses/descriptions/205.html (762 words)

	Explanation and Collective Computation
		The problem is that in conventional systems, explanation structures are based on intermediate states in processing which can be interpreted.
		Using a set of examples from a given problem domain, comprising inputs and their corresponding outputs, an artificial neural network can be trained to learn the relationship between the input-output pairs.
		The knowledge acquired about the problem domain during the training process is encoded within the ANN in two forms: 1) the network architecture itself (for example, number of "hidden" units) and 2) a set of numeric parameters ("weights").
	www.complexity.org.au /ci/vol02/explain/explain.html (3931 words)

	The Chiropractic Resource Organization
		That biological computation is lacking in the chiropractic subluxation theory is apparent since definitions are confined to linear observations of single level lesions.
		The implication might be that touch and sensory phenomenon derived from touch could contribute to the bodies ability to direct its movement; that, in a sense, the 'intent' of the body to respond to a sensory contact is part of the ability to direct itself...
		In other words, it is a computational response to the stimulus rather than an absolute all-or-none response through a wiring system; it is a directional movement determined by probability in the computational possibilities the brain has to offer.
	www.chiro.org /virgil/theories/computation.shtml (1703 words)

	Faculty of Informatics and Communication
		The problem is explored for a special case by reducing to the problem of binary sequence prediction with structural complexity as the criterion.
		The importance of emergent computation to global optimization is clear as an increasing number of algorithms are developed to mimic it (for example, simulated annealing, genetic and evolution algorithms).
		It was gradually realised that the problem of proposing such a structure was mainly about finding proper irreducible concepts to base the structure on and how to develop it without ever once referring to something that is not irreducible.
	www.infocom.cqu.edu.au /Staff/Victor_Korotkich/Publications/coec (4896 words)

	Instructional Television (Site not responding. Last check: 2007-10-20)
		Purpose: Problem solving should serve as the organizing feature of the mathematics curriculum as well as other areas of study and be applied to everyday activities.
		Solve problems that require the use of strategies (for example: working backwards; looking for patterns and relationships; guess and check; making tables, charts, and graphs; solving a simpler version of a problem; looking for similar problems; drawing a diagram; or creating a model).
		Students should be encouraged to estimate the solution of problems before computation or measurement is done, and to use estimation to determine the reasonableness of answers, and to recognize when an estimate is sufficient as an answer.
	www.nhptv.org /kn/itv/fwmathworks.htm (3139 words)

	LD OnLine :: Adapting Mathematics Instruction in the General Education Classroom for Students with Mathematics ...
		Computation involves not only memorization of basic facts, but also utilization of these facts to complete computational algorithms.
		Further adaptations and modifications in computational instruction include color coding of the desired function for the computation problem (Ariel, 1992), either ahead of time by the teacher or during independent practice by the student.
		This process serves as a reminder to the student to complete the desired function and also may be used as an evaluation device by the teacher to determine the student's knowledge of the mathematical symbols and processes they represent.
	www.ldonline.org /article/5928 (2732 words)

	The Turing Machine and Universal Computation (Site not responding. Last check: 2007-10-20)
		In 1900, at a mathematical conference in Paris, David Hilbert presented his famous 23 unsolved problems of Mathematics, the second problem of which was to determine whether the axioms of Mathematics were consistent or not.
		The problem can also be stated as how to find an algorithm that could determine whether a mathematical statement was true or false.
		A Quantum computer would be able to perform an infinite search in a finite amount of time and hence would solve the halting problem and would show the computability of incomputable functions.
	www.rit.edu /~maa2454/turing1.html (2867 words)

	The SETI@Home Problem
		The computation competition is aimed at encouraging clients to improve their rank by devoting more machines to the problem.
		A transcript of computation is something already referred to in the approach of using clients to test other clients; it is an output of such things as intermediate steps, internal state, register contents, and so on, sufficient to establish that the client was running the correct algorithm and not a patch.
		The transcripts of computation used in the previous approach could be considered proofs of correctness for a client's computation.
	www.acm.org /crossroads/columns/onpatrol/september2000.html (3333 words)

	2.2 Partitioning
		A focus on the computations that are to be performed can sometimes reveal structure in a problem, and hence opportunities for optimization, that would not be obvious from a study of data alone.
		Arrows represent exchanges of data between components during computation: the atmosphere model generates wind velocity data that are used by the ocean model, the ocean model generates sea surface temperature data that are used by the atmosphere model, and so on.
		Particularly in science and engineering applications, where the problem to be solved may involve a simulation of a complex physical process, the approximations and numerical techniques used to develop the simulation can strongly influence the ease of parallel implementation.
	www.mcs.anl.gov /dbpp/text/node16.html (1503 words)

	SPAMS Email Archive - Brian Sutton - The Mind-Body Problem in Computation (Site not responding. Last check: 2007-10-20)
		Mar 4, 2004 – Brian Sutton – The Mind-Body Problem in Computation
		************************************************************************ Title: The Mind-Body Problem in Computation** Abstract: In a purely functional programming language such as haskell, every statement is of the form identifier = value.
		Finally, the mind-body problem will be whisked away by philosopical chicanery.
	www-math.mit.edu /spams/spring2004/email4.htm (177 words)

	Resource: Teaching Math: A Video Library, K-4
		A fourth-grade class shares their reasoning in evaluating the appropriateness of different computational methods (base-ten blocks, calculators, mental math, or paper and pencil) to specific problems.
		First-graders are engaged in problem solving and measuring with both standard and nonstandard units.
		As students explain and justify their thinking and solutions throughout the excerpts, teachers emphasize that how a problem is solved is as important as its answer.
	www.learner.org /resources/series32.html (2332 words)

	ADUni - Theory of Computation - Problem Set 05 Solutions (Site not responding. Last check: 2007-10-20)
		We show this by reducing the problem of determining whether a CFG accepts everything to the problem of determing if the languages generated by two CFGs are equal by taking our input CFG and comparing it to the CFG that generates everything.
		We can simplify this problem by assigning each domino a value which is the number of 0s on the top row minus the number of zeros on the bottom row.
		We show that the problem is in NP by showing that it is verifiable in polynomial time.
	aduni.org /~dimitrik/aduni_stuff/2090/theory/ps05/ps05-ans.html (1368 words)

	Do Plants Practice Grid Computing?
		This might not sound much like what a computer does, but it is. In distributed computation, signals exchanged between components of the system define the process for solving a problem.
		Researchers are now exploring the possibility of using distributed computing with swarms of simple robots to carry out tasks, such as searching a landscape, more efficiently than a single, more sophisticated robot could manage.
		Plants must solve the problem of adjusting stomatal apertures to allow sufficient CO uptake for photosynthesis while preventing excessive water loss.
	radio.weblogs.com /0105910/2004/01/22.html (574 words)

	Abstracts
		We consider the problem of secure communication in a network with Byzantine faults for which the trust-graph, with vertices the processors and edges corresponding to certified public keys, is unknown except possibly to the adversary.
		In computer security, computational complexity is usually used to indicate a limitation or an impossibility.
		We consider the problem of secure communication in a network for which the trust-graph (with vertices the processors and edges corresponding to authentication channels) is unknown to all but one non-faulty processor, and show that we get secure communication if the trust-graph is sufficiently connected.
	www.cs.fsu.edu /~desmedt/survivability.html/results/abstract.html (1075 words)

	Math Content Standards K-4
		Problem solving is not a distinct topic but a process that should permeate the entire program and provide the context in which concepts and skills can be learned.
		As a result, computation, geometry, measurement, and problem solving tend to be taught in isolation.
		Clearly, paper-and-pencil computation cannot continue to dominate the curriculum or there will be insufficient time for children to learn other, more important mathematics they need now and in the future.
	www.allstar.fiu.edu /aero/Natmathk-4.htm (1935 words)

	G12FCO -- Formal Computation, problem class 1
		A Hamming Number [named after R. Hamming, who first discussed this exercise] is a positive integer which has no prime factor other than 2, 3 and 5; for example, 60 = 2 × 2 × 3 × 5 is such a number, but 42 [which is divisible by 7] isn't.
		Hamming's Problem is to find the first so-many [say, 1000] Hamming numbers.
		So one possible algorithm is to start at 1, count upwards, testing each number to see if it's Hamming, and stop when you have enough.
	www.maths.nottingham.ac.uk /personal/anw/G12FCO/prob1.html (692 words)

	With DNA, `Simple' Cells Perform Acrobatic Feats of Computation
		In 1994, computer theorist Leonard Adleman of the University of Southern California in Los Angeles revealed that he had found a way to harness the power of nature's genetic data bits -- DNA -- to solve a computation problem of his choosing.
		"The invention of the computer was fairly recent, and the invention of DNA computing is even more recent," she said in an interview.
		The ciliate DNA Landweber studies is flown from the University of Witten in Germany, where collaborator Hans Lipps "harvests" it, using a fine gauze sieve to separate the fat macronuclei from the smaller micronuclei.
	www.princeton.edu /~lfl/washpost.html (1032 words)

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