Since all problems in NP can be reduced to this problem it follows that for all problems in NP we can construct a non-deterministic Turing machine that decides the complement of the problem in polynomial time, i. e., NP is a subset of co-NP.

Since a typical piece of knitted fabric may have hundreds of wales, warp knitting is typically done by machine, whereas weft knitting is done by both hand and machine.

Since it is difficult to control machine pistols when they are fired in full automatic mode, in the 1970s, some manufacturers developed an " intermittent-fire " setting that fires a burst of three shots instead of a full-automatic stream.

; Compact size: Since p-code is based on an ideal virtual machine, a p-code program is often much smaller than the same program translated to machine code.

Since 2009, Sentinel has offered a machine described as a word processor, but in actuality it is more accurately a highly specialised microcomputer, used for accounting and publishing.

Since the machine was designed to operate on large data sets, the design also dedicated considerable circuitry to I / O.

Since the 1990s and onwards, this has led to severe contention between producers and aficionados of premium handmade cigars and cigarette manufacturing companies that create machine made, chemically formulated / altered products resembling cigars, and subsequently labeled as cigars.

Since WW I, there have been a variety of attempts to install armored gun shields on tripod-mounted machine guns or vehicle-mounted weapons to protect machine gunners.

:" Since the invention of this machine, Mr. Meikle and others have progressively introduced a variety of improvements, all tending to simplify the labour, and to augment the quantity of the work performed.

Since this machine, all computers designed with a microprocessor, personal computers, workstations even servers, will be called microcomputers.

Since a Befunge-93 program can only have a single stack and its storage array is bounded, the Befunge-93 language is, unlike most machine languages, not Turing-complete ( however, it has been shown that Befunge-93 is Turing Complete with unbounded stack word size ).

Since it was written in the C language, when that language was ported to a new machine architecture, Unix was also able to be ported.

Since the machine had been sold with a ' guarantee to fly ' Sir George succeeded in getting 15, 000 francs compensation from Zodiac.

Since it was quite easy to stack interconnections ( wires ) inside the embedding matrix, the approach allowed designers to forget completely about the routing of wires ( usually a time-consuming operation of PCB design ): Anywhere the designer needs a connection, the machine will draw a wire in straight line from one location / pin to another.

Since the invention of the first working sewing machine, generally considered to have been the work of Englishman Thomas Saint in 1790, the sewing machine has vastly improved the efficiency and productivity of fabric, clothing and needle industries.

Since the early 1950s almost all American presidents have had an autopen or robot machine for the automatic signing of a signature as an autograph machine for their letters, photographs, books, and even official documents.

Since the invention of the Fourdrinier machine in the 19th century, most paper has been made from wood pulp because of cost.

Since the machine had only 4k of RAM, this left very little room left over for the program's use, which was used for things like holding the score, or game options.

Since the machine only had 10 bits of address space, two of the address bits were unused and were sometimes used for data storage by interleaving data through the instructions.

Since the onigiri made by this machine came with nori already applied to the rice ball, over time the nori became unpleasantly moist and sticky, clinging to the rice.

Since then, and since the pure grain had gotten him divorced from every decent -- and even indecent -- group from Greenwich Village to the Embarcadero, he had become a sucker-rolling freight-jumper.

Since appeals to morality, to humanity, and to sanity have had such small effect, perhaps our last recourse is the deterrent example.

Since his seizure, Scotty had had little appetite ; ;

Since Mr. McKinley had to give a lecture, Rachel and Scotty drove home alone in the Plymouth.

Since she could not act, one part suited her as well as any other, and so she was the first person to offer Mr. Lincoln a glass of water, holding it up to the box, high above her head, to Miss Harris, who had asked for it.

Since the Santo Spirito hospital had taken only men, he had had no experience in the study of female anatomy ; ;

Since then, the flowers she had planted had spread all over the hill.

Since he had gross income of $600 or more, he must file a return in which he may claim an exemption deduction of $600.

Since the writer had established this democratic procedure in the beginning he had to go along with their decision -- after, of course, pointing out whether he thought their decision was a wise or an unwise one.

Since the writer had not noticed this characteristic in married students scattered throughout the various sections previous to this experiment, nor, as a matter of fact, in those who were continuing in `` single sections '', he can only conclude that there must have been something `` contagious '' within the specific group which caused this to occur.

Since the details of the elections were settled the change of government had no direct effect on the technical aspects of the elections, and may have been more important as an indication of royal displeasure with the U.N.F.P.

Since the strength of the Mexicans had been underrated, too small a posse had been collected, and since the deputy had not been provided with search warrants, MacPherson and his men decided it was much wiser to withdraw.

Since the magnitude of the plan made secrecy impossible, once the wheels had began to turn, persons controlling German industries, social institutions, and armed forces became, through their anti-Semitism or their tolerance of it, conscious accomplices of Hitler's crimes ; ;

Since Mrs. Calhoun remembered only that the marriage had been in the spring, he started to plod through several months.

Since then he had worked at this and that, though some said his main interest was gambling.

Since Election Day, Vice President Richard Nixon had virtually retired -- by his own wish -- from public view.

Since he possessed more power in an interdependent universe of living beings and dead spirits, the emperor had to use it for the benefit of the living.

Since we are assuming circular motion, let r ( t ) = R · u < sub > r </ sub >, where R is a constant ( the radius of the circle ) and u < sub > r </ sub > is the unit vector pointing from the origin to the point mass.

Since at a minimum the starting code address vector must always be valid on reset, systems commonly included some nonvolatile memory ( e. g. ROM ) starting at address zero to contain the vectors and bootstrap code.

Since the diagonal vector has a vertical component, the drive phase continues to provide some support against gravity and can be regarded as an extension of the support phase.

Since this construction works for any vector space V, we conclude that T is a functor from K-Vect to K-Alg.

Since the physicist's concept of force has a direction and a magnitude, it may be seen as a vector.

Since the typical vector operation would involve loading a small set of data into the vector registers and then running several operations on it, the vector system of the new design had its own separate pipeline.

Since this is an electromagnetic wave each electric field vector has a corresponding, but not illustrated, magnetic field vector that is at a right angle to the electric field vector and proportional in magnitude to it.

Since the propagation vector is proportional to the photon's momentum, the transverse propagation direction must remain the same in both regions.

Since the Poynting vector only occurs in Poynting's theorem as a divergence ∇ • S, the Poynting vector S is arbitrary to the extent that one can add a curl of a field F to S,

Since elements of W are necessarily elements of V, axioms 1, 2 and 5-8 of a vector space are satisfied.

Since then, the supercomputer market has focused much more on massively parallel processing rather than better implementations of vector processors.

Since a vector field is quite difficult to visualize at first, in elementary physics one may instead visualize this field with field lines.

Since the intensity or irradiance, I, of light is proportional to the square of the electric-field vector, the ellipticity becomes:

Since all these values are distinct, this is usually done using a bit vector.

However, the more difficult proof of the converse ( see below ) makes use of the vector space structure: Since both of the factors are vector spaces over Q, the tensor product can be taken over Q.

Since version 3. 0, Leveller includes vector shapes, which can be used for both modeling and coloration.

The set of ( p < sub > i </ sub >, n < sub > i </ sub >) is thus a sampling of a continuous vector field V. The implicit function f is found by integrating the vector field V. Since not every vector field is the gradient of a function, the problem may or may not have a solution: the necessary and sufficient condition for a smooth vector field V to be the gradient of a function f is that the curl of V must be identically zero.