
	Where results make sense

Topic: Nondeterministic algorithm

In the News (Wed 23 Dec 09)

Northern Trust

Marvin Harrison

Peter Chernin

Gary Locke

Match Play

Penelope Cruz

Mickey Rourke

AR Rahman

Danny Boyle

Hugh Jackman

	Nondeterministic algorithm - Wikipedia, the free encyclopedia
		In the theory of computation, a nondeterministic algorithm is an algorithm with one or more choice points where multiple different continuations are possible, without any specification of which one will be taken.
		Thus, different execution paths of the algorithm arise when it is applied to the same input / initial state, and these paths, when they terminate, generally produce different output / end in different final states.
		One way to simulate a nondeterministic algorithm N using a deterministic algorithm D is to treat sets of states of N as states of D.
	en.wikipedia.org /wiki/Nondeterministic (440 words)

	Algorithm
		Algorithm An algorithm is a well-defined set of instructions, finite in number, for accomplishing some task which, given...
		Nondeterministic algorithm In the theory of computation, a nondeterministic algorithm would be a hypothetical procedure,...
		Yarrow algorithm The Yarrow algorithm is a I Ching divination.
	www.brainyencyclopedia.com /topics/algorithm.html (1894 words)

	LURCH (Site not responding. Last check: 2007-10-21)
		Conventional algorithms for exploring a system's state space are deterministic, in that they have specific decision paths for mapping inputs to outputs.
		Nondeterministic algorithms, on the other hand, do not have such specific paths, allowing for the same inputs to result in different outputs.
		Nondeterministic analysis, however, may only explore a subset of the entire state space, and thereby miss some of the possible faults.
	www.yotor.org /wiki/en/lu/LURCH.htm (448 words)

	[No title]
		It is worth noting that given a problem, a nondeterministic algorithm for this problem does not solve it.
		Given a "yes" instance of the problem and a succint certificate for it, the nondeterministic algorithm only checks that the instance is indeed a "yes" instance of the problem by exploiting the certificate.
		Thus, it is not surprising that the behaviour of the algorithm in an AND and in an OR state is the same, since the space requirements in both states are the same.
	www.ida.liu.se /ext/etai/received/actions/007/!004.txt (1439 words)

	Nondeterministic polynomial time - Computing Reference - eLook.org
		The word "nondeterministic" suggests a method of generating potential solutions using some form of nondeterminism or "trial and error".
		NP is obviously a superset of P (polynomial time problems solvable by a deterministic Turing Machine in polynomial time) since a deterministic algorithm can be considered as a degenerate form of nondeterministic algorithm.
		If a problem A is in NP and a polynomial time algorithm for A could also be used to solve problem B in polynomial time, then B is also in NP.
	www.elook.org /computing/nondeterministic-polynomial-time.htm (184 words)

	[No title] (Site not responding. Last check: 2007-10-21)
		An algorithm to determine if a grammar is ambiguous.
		If the input size s is log n and the running time of an algorithm is is n, then the running time of the algorithm is an exponential function of the input size (n = 10^s).
		We used n as the input size when sorting a list of n keys, each of the keys would be represented in binary, and since there are n keys, there are at least n symbols in the input.
	www.unf.edu /public/cot4400/ree/Notes/ch9.old (398 words)

	[No title] (Site not responding. Last check: 2007-10-21)
		Another (but unfortunately exponential) algorithm: For all 13-bit numbers 0000000000000 to 1111111111111, try putting the corresponding integer into the first bin if the bit is a zero, the second bin if a one ¡Þ¤Z=ZÒZÿÿþÛ9ÿÿþ,ÿÿþÿÿþ/=J ÿÿþÿÿþió ¨Boolean satisfiabilityª¨óSuppose you have: n Boolean variables, A, B, C,...
		Here is a nondeterministic algorithm to solve the problem: For each Boolean variable, assign it the proper truth value.
		No one has ever found a deterministic polynomial-time algorithm for any of the NP problems No one has ever succeeded in proving that no such algorithm exists The status for some years now is this: Most computer scientists don't think a polynomial-time algorithm can exist, but no one knows for sure.
	cis.upenn.edu /~matuszek/cse121-2003/Lectures/45-difficult-problems.ppt (395 words)

	Nondeterministic Programs (Site not responding. Last check: 2007-10-21)
		The term Nondeterministic algorithm refers to a class of algorithms in which computational progress may correctly follow several different paths.
		Since we are satisfied that the algorithm computes the solution to a particular problem even if only one such path leads to termination with a solution, the implementation of nondeterministic algorithms requires a strategy for exploring the multiple paths that may emanate from some choice point.
		programs executing on a sequential machine that implement nondeterministic algorithms) have a distinctive continuation structure, since they must be able to run both forwards and backwards (forwards when successfully extending a partial solution, and backwards when failing to do so).
	www.cs.oberlin.edu /~rhyspj/classes/rit/abstrprac/lab9/lab99.html (158 words)

	Quals: Computer Theory and Algorithms - SEWiki
		A nondeterministic algorithm is much like a normal algorithm, with the addition of 3 O(1) operations: choice(S), which arbitrarily chooses an element from the set S, success(), which marks successful completion of the algorithm, and failure(), which marks unsuccessful completion.
		Kruskal's algorithm works by repeatedly choosing the globally lowest weighted edge that does not cause a cycle, until all nodes are intersected by the edges chosen.
		The shortest paths algorithm is a search in which an edge (that doesn't cause a cycle) is chosen each iteration such that the distance from the starting node to the newest node is minimized.
	www.cs.wm.edu /~coppit/wiki/index.php?title=Quals:_Computer_Theory_and_Algorithms (6730 words)

	nondeterministic algorithm (Site not responding. Last check: 2007-10-21)
		It is not random, as in randomized algorithm, or indeterminate.
		Nondeterministic algorithms compute the same class of functions as deterministic algorithms, but the complexity may be much less.
		Paul E. Black, "nondeterministic algorithm", from Dictionary of Algorithms and Data Structures, Paul E. Black, ed., NIST.
	www.nist.gov /dads/HTML/nondetermAlgo.html (220 words)

	Practical Natural Language Processing
		The algorithm is nondeterministic in the sense that it "chooses" which helper function it will use next.
		The predictor function could also be considered nondeterministic as the algorithm will still function even if the predictor only generates correct guesses (as opposed to generating an edge for every applicable rule in the grammar).
		The chart parsing algorithm returns a chart but we want to be able to extract any of the possible parse trees of the input string or section of the input string.
	sern.ucalgary.ca /courses/CPSC/533/W99/presentations/L2_23A_Curry_Lee (2909 words)

	Dictionary of Algorithms and Data Structures
		This is a dictionary of algorithms, algorithmic techniques, data structures, archetypical problems, and related definitions.
		We do not include algorithms particular to business data processing, communications, operating systems or distributed algorithms, programming languages, AI, graphics, or numerical analysis: it is tough enough covering "general" algorithms and data structures.
		Data Structures and Algorithms is a wonderful site with illustrations, explanations, analysis, and code taking the student from arrays and lists through trees, graphs, and intractable problems.
	www.nist.gov /dads (594 words)

	CS258
		The rate of growth of an algorithm is captured by the Big-O notation.
		Regardless of the actual time the algorithm may take to run, it is considered to be in the order of N O(N) if the running time grows linearly.
		To estimate the complexity for an algorithm, it is necessary to find the rate of growth of the number of steps in that algorithm.
	goanna.cs.rmit.edu.au /~linpa/258/goodpapers/p1.html (1845 words)

	[No title] (Site not responding. Last check: 2007-10-21)
		A nondeterministic algorithm has two phases: 1) A nondeterministic phase, some completely arbitrary string of characters is written into memory.
		Given a nondeterministic algorithm, A, the answer is "yes" if there is any run of A that can yield "yes".
		P is a subset of NP A deterministic algorithm is a special case of nondeterministic.
	www.unf.edu /public/cot3210/ree/Notes/np (570 words)

	[No title] (Site not responding. Last check: 2007-10-21)
		We have a nondeterministic algorithm that tries to guess a path from s to t, storing only the current node in its memory.
		First, observe that NL is in P. This is because PATH is in P (by a BFS algorithm), and every language in NL is logspace (and hence polytime) reducible to PATH.
		That is, we want to design a nondeterministic logspace algorithm for testing if node t is _not_ reachable from a node s in a given directed graph G. It's not at all obvious that this can be done.
	www.cs.sfu.ca /~kabanets/cmpt308/lectures/19.txt (510 words)

	NP
		Specifically, the focus of the study is to show that problems for which we have no known polynomial time algorithms are computationally related.
		Algorithms such that the result of every operation is uniquely defined are called deterministic algorithms.
		Although this interpretation may enable one to better understand nondeterministic algorithms, it is important to remember that a nondeterministic machine does not make any copies of an algorithm every time a choice is made.
	www.ecst.csuchico.edu /~amk/foo/csci356/notes/ch11/ch11.html (1257 words)

	[No title] (Site not responding. Last check: 2007-10-21)
		Class P is the class of decision problems that can be solved in polynomial time by a deterministic algorithm.
		Simple proof that the halting problem cannot be solved with an algoritm: Suppose that A is an algorithm that solves the halting problem.
		Trivailly, P is a subset of NP because a problem instance I can be solved nondeterministically by an algorithnm that uses an algorithm in P to generate a solution to problem I and then verifies it in polynomial time.
	www.eecis.udel.edu /~chester/courses/320-04f/notes24.txt (800 words)

	NP-Complete Problems
		This is a brief summary of NP-Completeness and approximate algorithms.
		Use brute force: may be the algorithm performance is acceptable for small input sizes.
		How good an approximate algorithm can be measure by worst case analysis with respect to opt(I) or input size.
	dcm.cl.uh.edu /yue/courses/csci5432/npcomplete.asp (742 words)

	CSC 432 Notes
		This means we can solve the problem in polynomial time if we had a nondeterministic machine to solve it (ha!).
		HAMPATH is in NP because we can give a nondeterministic algorithm to solve it in polynomial time.
		Typically such an algorithm is all about the verifier since guessing isn't particularly interesting or difficult.
	web.presby.edu /~wasmith/courses/432/notes/NPCompleteness.htm (637 words)

	26
		A nondeterministic algorithm guesses a Hamiltonian= cycle by choosing a sequence of vertices
		Howeve= r, it was shown by Pratt that a succinct certificate can be produced by a nondeterministic algorithm that can be verified in polynomial time (see Exercise 26.2).
		Cook proved Theorem 26.3.3 by constructing a CNF formula that, roughly speaking, modeled the action of the nondeterministic algorithm.
	www.ececs.uc.edu /~jpaul/472/book26.mht (2130 words)

	[No title]
		It nondeterministically choose one among > $greek(alpha)$ and $greek(beta)$ and evaluates it in w." This should be > rephrased.
		For example, in the case of SAT, given a satisfiable propositional formula $F$ and a truth assignment for the variables in $F$ that makes $F$ true, a nondeterministic algorithm for SAT checks that the assignment satisfies $F$.
		Notice also that AP is equal to PSPACE, that is, finding an alternating polynomial time algorithm for a given problem allows us to conclude that the problem can be solved in polynomial space.
	www.ida.liu.se /ext/etai/received/actions/007/!004.aml (1226 words)

	NP
		It is possible to construct a nondeterministic algorithm for which many different choice sequences lead to successful completions.
		That is, there is an NP algorithm for NP-Complete, but either there is not an NP algorithm or the problem is not a decision problem for NP-hard.
		If we have a polynomial time algorithm for the halting problem, then we could solve the satisfiablity problem in polynomial time using A and X as input to the algorithm for the halting problem.
	www.ecst.csuchico.edu /~amk/foo/csci356/notes/ch11/NP2.html (1239 words)

	Notes for 308-506, 18 September 2001
		A nondeterministic "algorithm" has many possible legal behaviors on a given input, so it is not possible to speak of what it will do, only what it might do.
		The central definition is that if N is a nondeterministic algorithm, the language L(N) is the set of input strings x such that it is possible for N to accept x.
		You may know that there is a poly-time algorithm that inputs an n-bit number, accepts all prime numbers with certainty, and rejects composite numbers with high probability.
	www.cs.mcgill.ca /~barring/notes/4.htm (1533 words)

	CIS 23: Questions on P/NP
		Here is a nondeterministic algorithm: (A is an array with n elements -- assume that A:=0 takes 1 step)
		Show that the Graph Coloring Problem is in NP by giving a nondeterministic algorithm for solving the problem.
		You must justify your answer with an algorithm or proof or formal argument.
	www.sci.brooklyn.cuny.edu /~gurwitz/cis23/f03/lastques.html (461 words)

	[No title]
		The algorithm returns “success” if they are, and “failure” if they’re not.
		Thus the development of an especially efficient algorithm often gives us added insight into the problem we are considering, an the resulting algorithm is not only efficient but simple and elegant.
		Ex: the complexity of an algorithm whose running time is a quadratic function of the problem size is O(n2).
	www.apl.jhu.edu /Classes/Notes/Hollywood/FOALec1S01.doc (448 words)

	CPSC 413 Textbook: Chapter 36 (Site not responding. Last check: 2007-10-21)
		algorithm; a randomized or nondeterministic algorithm can't be used as a verification algorithm, when we're trying to show that a language L can be ``verified in polynomial time.''
		Note that the function f mentioned here (as being computable in polynomial time) must be computable by a deterministic algorithm in polynomial time.
		Once again, the ``algorithm'' mentioned on Page 939 (in step 3 of the method sketched at the bottom of the page) must be a deterministic algorithm.
	pages.cpsc.ucalgary.ca /~eberly/Courses/CPSC413/1996/Textbook/chapter36.html (304 words)

	CSCI 6420 homework assignment 5
		Then there must be a nondeterministic polynomial time algorithm that takes an input x and tells you whether x is in S.
		Be careful about using a nondeterministic algorithm as a subroutine.
		Remember how nondeterministic algorithms work, by forking into a tree of computations, with the overall answer being yes just when there exists a thread that answers yes.
	www.cs.ecu.edu /~karl/6420/spr04/hw5.html (558 words)

	[No title] (Site not responding. Last check: 2007-10-21)
		Imagine that you are an algorithm, and they tell you to write either 0 or 1 without giving you any instructions how to perform the choice.
		A nondeterministic choice is performed by means of an intra-step query that algorithm poses to its environment.
		Again, the algorithm has no means to create a new object.
	www.cs.bu.edu /colloquium/LOG-05/05-16-11.txt (193 words)

	Theory
		The question: Is there an algorithm which when given any program and any set of input data for the program, can decide in advance whether or not the program will run forever (i.e.
		Theorem: There can be no such decision algorithm (assuming Church's thesis, which in practice everyone accepts and which says that every function that is computable by some sort of algorithm is computable by a Turing machine).
		A nondeterministic algorithm is one that assigns different cases of a problem to different processors.
	cis.stvincent.edu /swd/theory/theory.html (1013 words)

Try your search on: Qwika (all wikis)