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Topic: Halting problem

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	halting problem
		Alan Turing proved that the halting problem is undecidable: there's no way to construct an algorithm that is always able to determine whether another algorithm halts or not.
		Another amazing consequence of the undecidability of the halting problem is Rice's theorem, which states that the truth of any non-trivial statement about the function that is defined by an algorithm is undecidable.
		The undecidability of the halting problem relies on the fact that computers are assumed to have a memory of potentially infinite size.
	www.daviddarling.info /encyclopedia/H/halting_problem.html (517 words)

	Halting Problem is Solvable [rec.humor.funny]
		Furthermore, the problem can be solved within the time stipulated by the Graduate College for Ph.Ds or, in the worst case, with only a constant number of petitions for extensions.
		The halting problem was first formulated by Alan Turing, who observed a number of his graduate students being apparently busy all the time but never graduating.
		The hardest problem in NP hairy has been shown to be the problem of trying to claim standard deductions in the 1040 form).
	www.netfunny.com /rhf/jokes/89q4/halting.760.html (541 words)

	PlanetMath: halting problem
		The halting problem is to determine, given a particular input to a particular computer program, whether the program will terminate after a finite number of steps.
		In 1936, Alan Turing proved that the halting problem is undecideable; the argument is presented here informally.
		This is version 8 of halting problem, born on 2002-01-30, modified 2006-04-28.
	planetmath.org /encyclopedia/HaltingProblem.html (314 words)

	Cprogramming.com - Articles - Computability and the Halting Problem
		halting problem to follow the arguments in this discussion.
		This approach is called a reduction because the goal is to show how solving the halting problem could be reduced to solving another type of problem.
		The problem is that it has trouble determining if it won't ever be output.
	www.cprogramming.com /tutorial/computersciencetheory/computability.html (465 words)

	Is the Halting problem effectively solvable non-algorithmically?
		Halting problem for T: Given a Turing machine T, can one effectively decide, given any instantaneous description alpha, whether or not there is a computation of T beginning with alpha ([Me64], p256)?
		Informally, a problem is assigned to the complexity class P (deterministic polynomial-time) if the number of steps needed to solve it is bounded by some power of the problem's size.
		A problem is assigned to the complexity class NP (nondeterministic polynomial-time) if it permits a nondeterministic solution and the number of steps needed to verify the solution is bounded by some power of the problem's size.
	alixcomsi.com /Is_the_Halting_problem.htm (2836 words)

	General Halting Problem Problem
		In fact, the problem of whether or not an obfuscated version of a program is equivalent to the original version is also undecidable (it is the problem of program equivalence), but this fact is proven by reducing the halting problem to the problem of program equivalence, not vice versa.
		Halt is defined so that, on a tape that contains nothing but a description of a 0-argument Turing Machine, it runs and leaves a tape which contains only a 0 or a 1, depending on whether or not the given Turing Machine halts on an empty tape.
		Yes, the "general halting problem" proof is one that is commonly given in college courses.
	c2.com /cgi/wiki?GeneralHaltingProblemProblem (7653 words)

	BBC - h2g2 - The Halting Problem
		The halting problem describes why computers can't easily avoid crashing, or rather, why they can't predict when they are about to crash and avoid it.
		While it is true that the halting problem is currently one of the unsolvable problems in computing, there is also the possibility that in the future it won't matter.
		So while the halting problem is currently viewed as being unsolvable, there are now lots of tools appearing which can be used to make it a lot less relevant most of the time.
	www.bbc.co.uk /dna/h2g2/A1304939 (1771 words)

	CBofN - Glossary - H
		Halting Problem The problem of determining if a program halts or doesn't halt on a particular input.
		Halting Set The recursively enumerable set of Gödel numbers that correspond to programs that halt if given their own Gödel number as input.
		Holism The idea that ``the whole is greater than the sum of the parts.'' Holism is credible on the basis of emergence alone, since reductionism and bottom-up descriptions of nature often fail to predict complex higher-level patterns.
	mitpress.mit.edu /books/FLAOH/cbnhtml/glossary-H.html (230 words)

	The Busy Beaver Problem : A NEW MILLENNIUM ATTACK
		The machine halts when it reaches either a state, symbol pair for which there is no corresponding instruction, or it transitions into a explicitly defined halt state.
		The machine halts when it enters an explicitly defined halt state or no instruction can be found given the current state and read head symbol.
		A variant of the problem enforces the additional restriction that a machine can not be considered a Busy Beaver candidate unless the resulting pattern of 1's on the tape is in a contiguous sequence with the read head located at the left-most 1.
	www.cs.rpi.edu /~kelleo/busybeaver/problem.html (1285 words)

	anti-virus rants: how to spot snake oil using the halting problem (Site not responding. Last check: 2007-11-04)
		i blogged previously about how the halting problem is good for separating the possible from the impossible in the malware field, but i suspect it's still a little over most people's heads...
		finding all instances of the character 'a' or the string "dog") does not run into difficulties with the halting problem and is not snake oil (at least not as far as that particular claim is concerned)...
		any system that only claims to find/prevent some instances of something doesn't run into difficulties with the halting problem and is therefore probably not snake oil as far as that claim is concerned...
	anti-virus-rants.blogspot.com /2006/02/how-to-spot-snake-oil-using-halting.html (591 words)

	ha.ckers.org web application security lab - Archive » Why the turing halting problem dictates XSS filter evasion
		There is a common theory amongst the cryptographic community called the Turing Halting Problem.
		They know what has caused problems in the past, and they probably know a few variants of the same exploit code or vector, but they cannot know what they have not seen.
		Whichever problem it happens to be we still end up at the same place.
	ha.ckers.org /blog/20060603/why-the-turing-halting-problem-dictates-xss-filter-evasion (761 words)

	CS385, Halting Problem 2 (Site not responding. Last check: 2007-11-04)
		The second version of the halting problem is to determine, given a program P, whether P completes its computation on every possible input in a finite number of steps.
		Summary of the argument that the halting problem is undecidable
		Therefore, D is a decider for the first version of the halting problem, Halt.
	www.cs.bc.edu /~alvarez/Theory/halting2.html (457 words)

	The Halting Problem - Why you should care (Site not responding. Last check: 2007-11-04)
		The Halting Problem is very technical and I'm certainly not going to do the technical aspects of it any justice here (and the technically minded really aren't the audience I'm writing this for anyways).
		While changes to the current computing paradigm have been suggested for the purposes of better managing the problem, those changes would result in computers that are much more restrictive to users, developers, and probably innovation, and whether such changes will actually have their intended effect on the virus problem remains a matter of speculation.
		While The Halting Problem does effectively say that perfect virus detection is impossible, it doesn't say anything about how close to perfect we can get.
	www.claymania.com /halting-problem.html (586 words)

	The Halting Problem
		The Halting Problem is one of the simplest problems know to be unsolvable.
		Sketch of a proof that the Halting Problem is unsolvable
		Since K is a program, let us use K as the input to K. If H says that K halts then K itself would loop (that's how we constructed it).
	faculty.juniata.edu /rhodes/intro/theory2.htm (470 words)

	cs4fn: Mission:Impossible - The Halting Problem
		A problem that badly needs to be solved is how to be sure whether computer programs work properly.
		This is one of the most famous problems in computer science and is known as "The Halting Problem".
		Software verification is still a hard problem though and the race is on to improve such checking tools so they catch more and more problems for bigger and bigger programs.
	www.dcs.qmul.ac.uk /cs4fn/algorithms/haltingproblem.php (561 words)

	CSC 236: The Halting Problem (Site not responding. Last check: 2007-11-04)
		The Halting Problem is the problem of determining whether or not a given computer program terminates, as opposed to going into an infinite loop.
		Here is a sketch of a proof that the halting program is uncomputable; that is, there does not exist a program which takes another program as input (or as the initial value of a string variable) and correctly outputs whether or not it halts.
		Either PROBLEM is self-terminating or it is not.
	www.dgp.toronto.edu /~ajr/236/day/notes/halting.html (501 words)

	Chaitin, The Unknowable
		A more sophisticated example of an interesting instance of the halting problem is the conjecture called the Riemann hypothesis, probably the most famous open question in pure mathematics today.
		From the unsolvability of the halting problem it is easy to see that no truthful formal axiomatic system settles all instances of the halting problem.
		LISP Interpreter Run [[[[[ Proof that the halting problem is unsolvable by using it to construct a LISP expression that halts iff it doesn't.
	www.umcs.maine.edu /~chaitin/unknowable/ch4.html (1497 words)

	Halting Problem Discussions
		Another important consequence of the halting problem is being unable to know whether a given mathematical formula is a theorem or not (given a set of axioms and inference rules).
		If you had a tool that solves the halting problem for any program, it would automatically be able to solve all sorts of hard mathematics problems with no work.
		It doesn't even follow that all "programs" in that all halting programs do so in polynomial time with respect to their input size (which is the standard definition of polynomial and exponential time).
	c2.com /cgi/wiki?HaltingProblemDiscussions (14990 words)

	CS385, Halting Problem (Site not responding. Last check: 2007-11-04)
		The halting problem is to determine, given a program P and an input x to that program, whether P successfully completes its computation on x in a finite number of steps.
		The halting problem is a special case of the general problem of program verification, consisting of determining whether a given program behaves correctly according to its specification.
		This is not to say that it is not possible to write a program that will correctly determine halting for some reduced set of programs and inputs, just that no one program can solve the problem for all programs and inputs.
	www.cs.bc.edu /~alvarez/Theory/halting.html (417 words)

	halting problem (Site not responding. Last check: 2007-11-04)
		The problem of determining in advance whether a particular program or algorithm will terminate or run forever.
		The halting problem is the canonical example of a provably unsolvable problem.
		For example, if it is possible to record the complete state of the execution of the algorithm at each step and the current state is ever identical to some previous state then the algorithm is in a loop.
	burks.bton.ac.uk /burks/foldoc/19/51.htm (184 words)

	anti-virus rants: the halting problem - why you should care (Site not responding. Last check: 2007-11-04)
		the short version is that the halting problem tells us what is not possible in the computing world...
		creating a set of steps that will always determine if an arbitrary program performs function Y is reducible to the halting problem - all you have to do is say that function Y is a halt function and you'll see it's trivially true...
		creating a set of steps that will always determine if an arbitrary program is a virus is redcuible to the halting problem....
	anti-virus-rants.blogspot.com /2005/12/halting-problem-why-you-should-care.html (469 words)

	Mailgate: sci.logic: Re: Halting Problem Final Conclusion (Site not responding. Last check: 2007-11-04)
		The Halting Problem can only exist because > >> > of this same sort of pathological self-reference.
		If the Halting Problem is redefined (which does not > >> > refute anyone), then this redefined problem can be easily > >> > solved.
		> > [hint: it's obvious to everyone why you continually > refuse to answer the question: if you say yes then > your new improved halting problem is utterly dumb, > while if you say no then it's clear you have not > yet specified the problem you're talking about.
	mailgate.supereva.it /sci/sci.logic/msg19255.html (633 words)

	Computability and Complexity - The Halting Problem
		BAD tests whether the program represented by Q halts when given th e number Q as input (using the Halting Problem procedure, HALT, to perform the test).
		If the Halting problem procedure says that Q halts when started with input Q then BAD goes into a non-terminating loop.
		If the Halting problem procedure says that Q fails to halt when started with input Q then BAD prints a message and stops.
	www.csc.liv.ac.uk /~ped/teachadmin/algor/halt.html (731 words)

	What computers can't do
		As an example of his thought let's look at a proof that there is no way of telling in general once a computer has embarked on a calculation whether that calculation will terminate in an answer.
		This problem is known as the "Halting Problem for Turing machines" and was first proved in the 1937 paper
		The first main goal of his theory was an attempt on the classic problem of Phyllotaxis, the arrangement of leaves on a plant.
	pass.maths.org.uk /issue5/turing (1770 words)

	Cprogramming.com - Theoretical CS - The Halting Problem
		Think about whether there is a general solution to this problem -- a method that you could apply to any piece of C code in order to demonstrate that it will eventually come to a stop.
		Some programs might never halt when run on themselves, though -- so let's use DOES-HALT to write pseudo-code for a program that checks to see what happens when a program is given itself as input.
		In fact, the above argument is essentially a proof that the halting problem, as it is termed, cannot be solved in the general case.
	www.cprogramming.com /tutorial/computersciencetheory/halting.html (649 words)

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