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problem and computational
Algorithm analysis is an important part of a broader computational complexity theory, which provides theoretical estimates for the resources needed by any algorithm which solves a given computational problem.
In the field of artificial intelligence, the most difficult problems are informally known as AI-complete or AI-hard, implying that the difficulty of these computational problems is equivalent to solving the central artificial intelligence problem — making computers as intelligent as people, or strong AI.
It is a challenge to functionalism and the computational theory of mind, and is related to such questions as the mind-body problem, the problem of other minds, the symbol-grounding problem, and the hard problem of consciousness.
* Collision detection, the computational problem of detecting the intersection of two or more objects
In this context, a computational problem is understood to be a task that is in principle amenable to being solved by a computer ( i. e. the problem can be stated by a set of mathematical instructions ).
Informally, a computational problem consists of problem instances and solutions to these problem instances.
A key distinction between analysis of algorithms and computational complexity theory is that the former is devoted to analyzing the amount of resources needed by a particular algorithm to solve a problem, whereas the latter asks a more general question about all possible algorithms that could be used to solve the same problem.
A computational problem can be viewed as an infinite collection of instances together with a solution for every instance.
The input string for a computational problem is referred to as a problem instance, and should not be confused with the problem itself.
In computational complexity theory, a problem refers to the abstract question to be solved.
For this reason, complexity theory addresses computational problems and not particular problem instances.
When considering computational problems, a problem instance is a string over an alphabet.
In computability theory and computational complexity theory, a decision problem is a question in some formal system with a yes-or-no answer, depending on the values of some input parameters.
" Difficult ", in this sense, is described in terms of the computational resources needed by the most efficient algorithm for a certain problem.
A distributed system may have a common goal, such as solving a large computational problem.

problem and universality
In other words, the general problem of Diophantine analysis is blessed or cursed with universality, and in any case is not something that will be solved except by re-expressing it in other terms.
Although Immanuel Kant's Critique of Judgement ( 1790 ) did formulate a non-relativistic idea of aesthetical universality, where both personal pleasure and pure beauty coexisted, it was concepts such as class taste that began the attempt to find essentially sociological answers to the problem of taste and aesthetics.

problem and is
That is why the form itself becomes a preoccupation, because it exists as a problem separate from the material it accommodates.
The specific analogy to the dilemma of love is the problem of the `` breakthrough '' in the realm of art.
This is an unsolved problem which probably has never been seriously investigated, although one frequently hears the comment that we have insufficient specialists of the kind who can compete with the Germans or Swiss, for example, in precision machinery and mathematics, or the Finns in geochemistry.
But the problem is one which gives us the measure of a man, rather than a group of men, whether a group of doctors, a group of party members assembled at a dinner to give their opinion, or the masses of the voters.
In the incessant struggle with recalcitrant political fact he learns to focus the essence of a problem in the significant detail, and to articulate the distinctions which clarify the detail as significant, with what is sometimes astounding rapidity.
The problem is to remove the accretions and thereby uncover the order that was always there.
Moral dread is seen as the other face of desire, and here psychoanalysis delivers to the writer a magnificent irony and a moral problem of great complexity.
The maturity in this point of view lies in its recognition that no basic problem is ever solved without being clearly understood.
The problem is rather to find out what is actually happening, and this is especially difficult for the reason that `` we are busily being defended from a knowledge of the present, sometimes by the very agencies -- our educational system, our mass media, our statesmen -- on which we have had to rely most heavily for understanding of ourselves ''.
Ptolemy's problem is to forecast where, against the inverted bowl of night, some particular light will be found at future times.
The distances of these points of light is a problem he cannot master, beyond crude conjectures as to the orderings of the planetary orbits viewed outward from earth.
This is a problem to be solved not by America alone, but also by every nation cherishing the same ideals and in position to provide help.
The problem, in other words, is strictly a chronological one.
The problem of NATO is not one of machinery, of which there is an abundance, but of the will to use it.
Our problem, therefore, is to devise processes more modest in their aspirations, adjusted to the real world of sovereign nation states and diverse and hostile communities.
The main question raised by the incident is how much longer will UN bury its head in the sand on the Congo problem instead of facing the bitter fact that it has no solution in present terms??
The only real problem is to devise a plan whereby the owners of the above-water land can develop their property without the public losing its underwater land and the right to its development for public use and enjoyment.
Biggest organizational problem, he adds, is setting up CDC units in rock-ribbed Democratic territory.
If they are to be commended for foresight in their planning, what then is the judgment of a town council that compounds this problem during the planning stage??
The new column by Maurice Stans regarding business scandals, is fair and accurate in most respects and his solution to the problem has some merit.
The whole problem of `` peaceful coexistence and peaceful competition '' with the capitalist world is in the very center of this Congress.
But this is not the real problem ; ;

problem and solved
The rustling problem was by no means solved.
He studied the problem for a few seconds and thought of a means by which it might be solved.
At this moment Mando came hurrying up to announce that the problem was solved and all Norton had to do was to sign a sheaf of papers.
This method in general solved the problem of obtaining fairly equal concentrations of reactants in each of the six cells from a set.
It should also be recognized that the problem of rural tenancy cannot be solved by administrative decrees alone.
Conceivably the submarine defense problem can be solved by sufficient forces.
( The largest problem that could be solved without the use of the intermediate output and input was two simultaneous equations, a trivial problem.
This problem was not solved by the time Atanasoff left the university for war-related work.
Isaac Asimov solved the same communication problem with the hyper-wave relay in the Foundation series.
Apple solved this problem using an AppleBus-like solution, using a single port on the back of the computer into which the user could plug an adaptor for any given cabling system.
An analog computer is a form of computer that uses the continuously changeable aspects of physical phenomena such as electrical, mechanical, or hydraulic quantities to model the problem being solved.
Above 0. 3, the problem should be solved by using compressible aerodynamics.
To call a problem AI-complete reflects an attitude that it would not be solved by a simple specific algorithm.
J. K. Starley ( nephew of James Starley ), J. H. Lawson, and Shergold solved this problem by introducing the chain drive ( originated by the unsuccessful " bicyclette " of Englishman Henry Lawson ), connecting the frame-mounted cranks to the rear wheel.
As the problem of P ≟ PSPACE has not yet been solved, the proof of inequality between BQP and classes mentioned above is supposed to be difficult.
This problem can also be solved in polynomial time, and in fact is complete for the class NL.
This problem is solved by the polynomial-time Horn-satisfiability algorithm, and is in fact P-complete.
The problem of deciding whether a set of Horn clauses is satisfiable is in P. This problem can indeed be solved by a single step of the Unit propagation, which produces the single minimal model of the set of Horn clauses ( w. r. t.
As mentioned briefly above, though the problem is NP-complete, many practical instances can be solved much more quickly.
Although this problem seems easier, it has been shown that if there is a practical ( randomized polynomial-time ) algorithm to solve this problem, then all problems in NP can be solved just as easily.

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