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* Since NP-complete problems transform to each other by polynomial-time many-one reduction ( also called polynomial transformation ), all NP-complete problems can be solved in polynomial time by a reduction to H, thus all problems in NP reduce to H ; note, however, that this involves combining two different transformations: from NP-complete decision problems to NP-complete problem L by polynomial transformation, and from L to H by polynomial Turing reduction ;
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Since and NP-complete
* Since L is NP-complete, and hence the hardest in class NP, also problem H is at least as hard as NP, but H does not have to be in NP and hence does not have to be a decision problem ( even if it is a decision problem, it need not be in NP );
Since the ATPG problem is NP-complete ( by reduction from the Boolean satisfiability problem ) there will be cases where patterns exist, but ATPG gives up since it will take an incredibly long time to find them ( assuming P ≠ NP, of course ).
To translate this to a subgraph isomorphism problem, simply let H be the complete graph K < sub > k </ sub >; then the answer to the subgraph isomorphism problem for G and H is equal to the answer to the clique problem for G and k. Since the clique problem is NP-complete, this polynomial-time many-one reduction shows that subgraph isomorphism is also NP-complete.
Since and problems
Since morale is closely related to pattern maintenance and integration, the higher the morale and solidarity, the better the system can solve the problems of the system.
Since experience indicates that effluents from oxidation ponds do not create major problems at these BOD concentrations, the goal for the effluent quality of the accelerated treatment system was the same as from conventional oxidation ponds.
Since many AI problems have no formalisation yet, conventional complexity theory does not allow the definition of AI-completeness.
Since the end of the Second World War, the development of computers has allowed a systematic development of computational chemistry, which is the art of developing and applying computer programs for solving chemical problems.
Since its construction, the tunnel has faced several problems.
Since the 1980s, the more difficult problems of implementing valence bond theory into computer programs have been solved largely, and valence bond theory has seen a resurgence.
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 1979 the Convention on Long-range Transboundary Air Pollution has addressed some of the major environmental problems of the UNECE region through scientific collaboration and policy negotiation.
Since the end of the Second World War, the development of computers has allowed a systematic development of computational chemistry, which is the art of developing and applying computer programs for solving chemical problems.
Since the USSR's collapse, Russia faced many problems that free market proponents in 1992 did not expect.
Since the occurrence and severity of these health problems is largely hereditary, breeders are working to eliminate these.
Since 2003, security problems have blocked efforts to establish new enterprises.
Since Merced was the first EPIC processor, the development effort encountered more unanticipated problems than the team was accustomed to.
Since Rogue was having problems with Gambit, the two of them go on a road trip to ease their minds.
" For this, Heaven inflicted upon him kidney stones, painful flatulence, and other gastric problems, saying, " Since he showed no pity, let us bring suffering upon him ".
'" For this, Heaven removed the gastric problems from him, saying, " Since he has shown compassion, let us be compassionate with him ".
Since the beginning of modern philosophy during the seventeenth century, problems that were not originally considered within the bounds of metaphysics have been added to its purview, while other problems considered metaphysical for centuries are now typically subjects of their own separate regions in philosophy, such as philosophy of religion, philosophy of mind, philosophy of perception, philosophy of language, and philosophy of science.
( Since the sub-structure is usually represented in the computer by a set of integer variables with constraints, these problems can be viewed as special cases of constraint satisfaction or discrete optimization ; but they are usually formulated and solved in a more abstract setting where the internal representation is not explicitly mentioned.
Since many American " suburbs " had become cities about 50 or more years ago, it became necessary to start making a distinction between the new communities, traditionally referred to as suburban, and the aging ones that were actually cities and sometimes dealing with the same problems that the central city had.
Since manufacturers are the ' cheapest cost avoiders ', because they have a greater chance to seek out problems, it makes sense to give them the incentive to guard against product defects.
Since 2009, non-profit organization Global Heritage Fund ( GHF ) has been working to protect and preserve Ur against problems of erosion, neglect, inappropriate restoration, and war and conflict.
Since phospholipase enzymes play a significant part in the cascade leading to the inflammatory and pain response, their inhibition could lead to relief of problems from scorpion envenomation.
Since 1996 most automobiles have employed an on-board computer and various sensors to detect mechanical problems.
Since and transform
Since Bragg's law does not interpret the relative intensities of the reflections, however, it is generally inadequate to solve for the arrangement of atoms within the unit-cell ; for that, a Fourier transform method must be carried out.
Since, we now have an expression for the Laplace transform of in terms of's Laplace transform:
Since the Laplace transform of 1 is, we continue:
Since the 1920s it had been suspected that the Sun shines because of nuclear fusion reactions that transform hydrogen into helium and release energy.
Since then and particularly from 1963 onwards, there have been continuous attempts to transform the ethnic make-up of the region.
Since Rader's algorithm only depends upon the periodicity of the DFT kernel, it is directly applicable to any other transform ( of prime order ) with a similar property, such as a number-theoretic transform or the discrete Hartley transform.
Since the heroes and the gimmicks tend to repeat from film to film, only a great villain can transform a good try into a triumph.
Since polyps often take 10 to 15 years to transform into cancer, in someone at average risk of colorectal cancer, guidelines recommend 10 years after a normal screening colonoscopy before the next colonoscopy.
Since 2006, there has been debate whether or not to transform RTHK into a public corporation.
Since 2009, the investments have begun to transform Devonport-physically, socially, demographically.
Since the inverse Fourier transform is
Since the portal transforms travelers into a sapient species found in the destination world ( which is how Lindesfarne became a hedgehog and Danielle a rabbit, though both were born humans in “ our ” world and had counterparts of those other species in the Kevin and Kell world ), travelers from that world usually transform into humans, but Catherine and her son transformed into dolphins instead ( indicating that dolphins are, in fact, sapient, and perhaps more so than humans ).
Since the Scandinavian version can transform himself into a horse-like kelpie, he is also called Bäckahästen ( the " brook horse ").
Since most individuals who were elected to political office were given membership in the Roman Senate, this development helped to transform the senate from a body of Patricians into a body of Plebeian and Patrician aristocrats.
Since all of these steps reduce the degrees of vertices in the graph, vertices may transform from being high-degree ( degree > K ) to low-degree during the algorithm, enabling them to be simplified or coalesced.
Since Lagrangian mechanics is based on generalized coordinates, transformations of the coordinates q → Q do not affect the form of Lagrange's equations and, hence, do not affect the form of Hamilton's equations if we simultaneously change the momentum by a Legendre transform into
Since a digital computer is a discrete system, the Laplace transform is replaced with the Z-transform.
Since moduli are defined by and J must transform as listed above under, only those moduli paired with 2-form basis elements of the correct parity under survive.
Since it is often desirable to work with more than one basis for a vector space, it is of fundamental importance in linear algebra to be able to easily transform coordinate-wise representations of vectors and linear transformations taken with respect to one basis to their equivalent representations with respect to another basis.
Since one period of the function contains all of the unique information, it is sometimes convenient to say that the DTFT is a transform to a " finite " frequency-domain ( the length of one period ), rather than to the entire real line.
Since 2001, the ground has seen the building of the new stand and then the hard work of Geoffrey Rainey, Michael Clancy and a host of other volunteers who have once again helped transform the ground.
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