Help


[permalink] [id link]
+
Page "Probabilistically checkable proof" ¶ 4
from Wikipedia
Edit
Promote Demote Fragment Fix

Some Related Sentences

Completeness and L
* L. Blum, M. Shub, S. Smale, “ On a Theory of Computation Over the Real Numbers ; NP Completeness, Recursive Functions and Universal Machines ,” FOCS ; 88 ; Bulletin of the AMS, Vol.

Completeness and for
Completeness of the market is also important because in an incomplete market there are a multitude of possible prices for an asset corresponding to different risk-neutral measures.
Completeness is a common property of market models ( for instance the Black – Scholes model ).
* MPC Java-based implementation A Java-based implementation of the MPC protocol based on Michael. B, Shafi. G and Avi. W's theorem (" Completeness theorems for non-cryptographic fault-tolerant distributed computation ") with Welch-Berlekamp error correcting code algorithm to BCH codes.
How to Play any Mental Game, or A Completeness Theorem for Protocols with Honest Majority, Proceedings of STOC 1987, pp. 218 – 229, 1987.

Completeness and some
Completeness of first-order logic was first explicitly established by Gödel, though some of the main results were contained in earlier work of Skolem.
Completeness seems to be at the center of shalom as we will see in the meaning of the term itself, in some derivatives from its root, shalam, in some examples of its uses in Jewish and Christian Scriptures, and in some homophone terms from other Semitic languages.

Completeness and V
Completeness and accuracy is described by the weakest apparent magnitude V ( largest number ) and the accuracy of the positions.
This was quickly followed by a French translation, in which Hilbert added V. 2, the Completeness Axiom.
* V. 2, the Axiom of Completeness, has been replaced by:

Completeness and with
* Completeness: if the string is in the language, the prover must be able to give a certificate such that the verifier will accept with probability at least 2 / 3 ( depending on the verifier's random choices ).
" The Gelukpa allow that it is possible to take the mind itself as the object of meditation, however, Zahler reports, the Gelukpa discourage it with " what seems to be thinly disguised sectarian polemics against the Nyingma Great Completeness and Kagyu Great Seal meditations.
Tsogyel, though fairly obviously a transformation of an older Bön figure, Bönmo Tso ( female Bön practitioner of the lake ), whom she debates in her " autobiography ", also preserves the Great Completeness traditions shared by Bön with Tibet's earliest Buddhist tradition.

Completeness and ),
* Zach, Richard, ( 1999 ), " Completeness before Post: Bernays, Hilbert, and the development of propositional logic ", Bulletin of Symbolic Logic, 5 ( 3 ): 331-366.

If and x
* If it is required to use a single number X as an estimate for the value of numbers, then the arithmetic mean does this best, in the sense of minimizing the sum of squares ( x < sub > i </ sub > − X )< sup > 2 </ sup > of the residuals.
If F is algebraically closed and p ( x ) is an irreducible polynomial of F, then it has some root a and therefore p ( x ) is a multiple of x − a.
If P is a program which outputs a string x, then P is a description of x.
If M is a Turing Machine which, on input w, outputs string x, then the concatenated string < M > w is a description of x.
If F is an antiderivative of f, and the function f is defined on some interval, then every other antiderivative G of f differs from F by a constant: there exists a number C such that G ( x ) = F ( x ) + C for all x.
If the filter shows amplitude ripple within the passband, the x dB point refers to the point where the gain is x dB below the nominal passband gain rather than x dB below the maximum gain.
* The Lusternik – Schnirelmann theorem: If the sphere S < sup > n </ sup > is covered by n + 1 open sets, then one of these sets contains a pair ( x,x ) of antipodal points.
* If G is a locally compact Hausdorff topological group and μ its Haar measure, then the Banach space L < sup > 1 </ sup >( G ) of all μ-integrable functions on G becomes a Banach algebra under the convolution xy ( g ) = ∫ x ( h ) y ( h < sup >− 1 </ sup > g )( h ) for x, y in L < sup > 1 </ sup >( G ).
If a Banach algebra has unit 1, then 1 cannot be a commutator ; i. e., for any x, y A.
If x is held fixed, then the Bessel functions are entire functions of α.
If the exponent r is even, then the inequality is valid for all real numbers x.
If x is a member of A, then it is also said that x belongs to A, or that x is in A.
If ( x < sub > 1 </ sub >, x < sub > 2 </ sub >, x < sub > 3 </ sub >) are the Cartesian coordinates and ( u < sub > 1 </ sub >, u < sub > 2 </ sub >, u < sub > 3 </ sub >) are the orthogonal coordinates, then

If and
If the method is applied to an infinite sequence ( X < sub > i </ sub >: i ω ) of nonempty sets, a function is obtained at each finite stage, but there is no stage at which a choice function for the entire family is constructed, and no " limiting " choice function can be constructed, in general, in ZF without the axiom of choice.
If ~ and ≈ are two equivalence relations on the same set S, and a ~ b implies a ≈ b for all a, b S, then ≈ is said to be a coarser relation than ~, and ~ is a finer relation than ≈.
If f: X → Y is a continuous map, x < sub > 0 </ sub > X and y < sub > 0 </ sub > Y with f ( x < sub > 0 </ sub >) = y < sub > 0 </ sub >, then every loop in X with base point x < sub > 0 </ sub > can be composed with f to yield a loop in Y with base point y < sub > 0 </ sub >.
The intermediate value theorem states the following: If f is a real-valued continuous function on the interval b, and u is a number between f ( a ) and f ( b ), then there is a c b such that f ( c ) = u.
# If x is a variable, then x Λ
# If x is a variable and M Λ, then ( λx. M ) Λ
# If M, N Λ, then ( M N ) Λ
# If N is a neighbourhood of x, then x N. This means every point belongs to every neighbourhood of the point.
If X and Y are subsets of the real numbers, d < sub > 1 </ sub > and d < sub > 2 </ sub > can be the standard Euclidean norm, || · ||, yielding the definition: for all ε > 0 there exists a δ > 0 such that for all x, y X, | x − y | < δ implies | f ( x ) − f ( y )| < ε.
So, formally, a language L is NP-hard if ∀ L < sup >'</ sup > NP, L < sup >'</ sup >L. If it is also the case that L is in NP, then L is called NP-complete.
If S is compact but not closed, then it has an accumulation point a not in S. Consider a collection consisting of an open neighborhood N ( x ) for each x S, chosen small enough to not intersect some neighborhood V < sub > x </ sub > of a.
# If x Null ( A ) and y Null ( A ), then x + y Null ( A ).
# If x Null ( A ) and c is a scalar, then c x Null ( A ), since ( cA ) x = c ( Ax ).
If I is an index set and X < sub > I </ sub > is the set of indeterminates X < sub > i </ sub > for i I, then a monomial X < sup > α </ sup > is any finite product of elements of X < sub > I </ sub > ( repetitions allowed ); a formal power series in X < sub > I </ sub > with coefficients in a ring R is determined by any mapping from the set of monomials X < sup > α </ sup > to a corresponding coefficient c < sub > α </ sub >, and is denoted.
If the last equality is satisfied for all t < sub > 1 </ sub >, t < sub > 2 </ sub > I, the geodesic is called a minimizing geodesic or shortest path.
If W = V, then one can also pair the covector w * V * with the vector v V via ( w *, v ) → w *( v ), which is the duality pairing between V and its dual, sometimes called the inner product.
If Q is a point of S < sup > n </ sup > and E a hyperplane in E < sup > n + 1 </ sup >, then the stereographic projection of a point P S < sup > n </ sup >

0.848 seconds.