The Cook – Levin theorem states that the Boolean satisfiability problem is NP-complete, and in fact, this was the first decision problem proved to be NP-complete.

SAT was the first known NP-complete problem, as proved by Stephen Cook in 1971 ( see Cook's theorem for the proof ).

It is widely believed that PSPACE-complete problems are strictly harder than any problem in NP, although this has not yet been proved.

Labour shortages proved to be a more frequent problem.

Soon the notoriety of Bimba's Capoeira proved to be a problem to traditional capoeiristas, who were gradually losing visibility and were still distrusted by society.

The riveted mail armour worn by the opposing Sudanese Madhists did not have the same problem but also proved to be relatively useless against the firearms of British forces at the battle of Omdurman.

The Stammbaumtheorie proved to be very productive for comparative linguistics, but didn't solve the major problem of studying the origin of language: the lack of fossil records.

The film's setting proved to be a potential problem for Carpenter, who needed to create a decaying, semi-destroyed version of New York City on only a shoe-string budget.

The climate and environment of Venice has proved to be a problem for frescoes and other works of art in the city for centuries.

This problem has subsequently proved to be a stumbling block to a negotiated settlement of the ongoing conflict.

If an isomorphism can be found from a relatively unknown part of mathematics into some well studied division of mathematics, where many theorems are already proved, and many methods are already available to find answers, then the function can be used to map whole problems out of unfamiliar territory over to " solid ground " where the problem is easier to understand and work with.

Newton proved to be a continual problem for the crew of Pegasus.

Unfortunately performance proved to be a major problem, and a number of architectural changes were made in order to solve this problem.

Hence, the decision problem for Presburger arithmetic is an example of a decision problem that has been proved to require more than exponential run time.

Use of this wide shift proved to be a problem for Amateur Radio operations.

The pure-group languages were the first interesting family of regular languages for which the star height problem was proved to be decidable.

Larry Stockmeyer has proved that for every # P problem P there exists a randomized algorithm using oracle for SAT, which given an instance a of P and ε > 0 returns with high probability a number x such that.

Another studio actor who proved to be a problem for Jack Warner was George Raft.

The motor, the direction of which could be reversed by reversing its polarity, proved the solution to the last remaining problem in alternating-current motors.

Members of other socialist groups also joined it, and the special relationship with the SLP soon proved to be a problem.

Conway in the 1970s, proved that a natural generalization of the Collatz problem is algorithmically undecidable.

The race problem has tended to obscure other, less emotional, issues which may fundamentally be even more divisive.

But no single planetary problem ever required of Ptolemy more than six epicycles at one time.

In any case I do not intend to let the present occasion pass without dealing more directly with the problem of implementing good intentions.

For them only a little more needed to be learned, and then all physical knowledge could be neatly sorted, packaged and put in the inventory to be drawn on for the solution of any human problem.

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.

But more than one conscientious researcher has been inhibited from completely frank discussion of the available evidence by the less excusable fact that fallout has been made a political issue as well as a scientific problem.

No satisfactory solution has been found, but this is due more to the difficulties inherent in the problem than to a lack of interest or diligence on the part of the assessors.

A mathematical formula is nothing more than a pattern for solving a specific problem.

But if space and money are no problem and small children are not on hand every day, it is certainly more restful to have your pool and entertainment area removed from the immediate environs of the house.

It is more than just lack of dance training that is our problem, for just as gymnastics can learn from dance, dance has some very important things to learn from gymnastics.

So we asked such men in major companies in the design field to offer their opinions on the `` dual-road-up '' problem -- and more importantly -- their solutions.

After this brief discussion of neo-, paleocortical, and cortico-hypothalamic relations, let us return once more to the problem of hypothalamic balance and its physiological and pathological significance.

This will be more or less our general method for the second problem.

Centrally, however, the administrative problem was more complex and the sheer prestige of office was very likely an unfair advantage.

The closed molding of flexible urethane foams has been a problem ever since the introduction of the material ( molding in open molds was more feasible ).

This is a problem to which leaders of opinion, both Negro and white, should devote far more attention.

And then, some churchmen remarked, there is a more classical church-state problem:

The problem is not merely that more `` outside teachers '' are needed but that a different brand is called for.

It is particularly interesting that those who framed the report should refer to `` the organization which actually owns the university '': this seems to show an awareness of the fact that there is more to the problem than the ordinary issue of clerical-lay tension.

The problem becomes even more complex where an enterprise is engaged in the manufacture of a wide variety of other goods in addition to the heavy electrical equipment.

The quest for holism leads most anthropologists to study a particular place, problem or phenomenon in detail, using a variety of methods, over a more extensive period than normal in many parts of academia.

Another problem was that the gradual identification of more and more chemically similar and indistinguishable lanthanides, which were of an uncertain number, led to inconsistency and uncertainty in the numbering of all elements at least from lutetium ( element 71 ) onwards ( hafnium was not known at this time ).

Johnston's initial call upon the governors for more men did not result in many immediate recruits but Johnston had another, even bigger, problem since his force was seriously short of arms and ammunition even for the troops he had.

The Bohr model of the atom fixed the problem of energy loss from radiation from a ground state ( by declaring that there was no state below this ), and more importantly explained the origin of spectral lines.