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HOKIE: Introduces the Plookup algorithm

The basic idea The problem Plookup tries to solve is toprove, given two sets, that elements of one set are in the other. Given twosets t and f, s is

The basic idea

The problem Plookup tries to solve is toprove, given two sets, that elements of one set are in the other. Given twosets t and f, s is the sorted result of f. If the element in T appears at leastonce in F. To determine whether an element in F is included in T, we only needto compare the set of element differences:

HOKIE: Introduces the Plookup algorithm

For example, t is the set {1,4,8}, and thedifference set of elements is {3, 4}, which are 4-1, 8-4 respectively. If sconsists only of elements in t and each element occurs at least once, such as{1,1,4,8,8,8}, the set of differences of elements is also {3,4}. If theelements in S are not exactly elements in T, it does not follow that theelements in S are in the set of T even if the set of element differences is thesame. For example, s is {1, 5,5, 5, 8, 8}, and the difference set of elementsis {3,4}, 8-5, 5-1, respectively.

A random factor can be introduced todetermine the dependency of two sets by adding the preceding and followingelements.

Defining polynomial

On the basis of the basic idea, twopolynomials F and G are defined:

HOKIE: Introduces the Plookup algorithm

If F and G are equivalent to each other,the following conditions are true:

• F is a member of t

• s is the union of (f, t) and is orderedby the elements in t

If this is true, it follows that the twopolynomials are equal. F polynomials can be viewed as having two parts, twoserial products. You can view this as a multiplication of the elements in t.You can view this as a multiplication of the elements of f. Since the elementsin F belong to t, the multiplication of the elements in F can be imagined as amultiplication of the same elements. Conversely, beC.USe of the random factorsof beta and gamma, the two conditions satisfied can also be deduced from the Fand G equivalents.

On the basis of defining polynomials, theproblem can be transformed into two polynomials equal.

Plookup agreement

If you know f and t, you can sort it to gets. Since S is a combination of f and t, s can be represented by two functions,h1 and h2. The key is step 4, which defines the Z function:

• Z(g) = 1 - I started with 1

• Z(x) is the quotient of two polynomials

• Z(g^(n+1)) = 1 - n+1, both polynomialsare equal

HOKIE: Introduces the Plookup algorithm

The verifier, in addition to looking at theZ function, also looks at the H1 / H2 continuity.

conclusion

Plookup proposes a protocol for proving thecorrectness of a function operation in the case of explicit input/output. Theinput and output are defined as lookup tables. The calculated input/result iscorrect as long as it is in the lookup table. Plookup and Plonk adopt the sameidea, Plookup defines the polynomial representation of the problem, and provesthe recursive representation and boundary of the Z function.

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