Open: The opening algorithm Open(pp,C,P(x),x0)→(ev,π)\text{Open}(\text{pp}, C, P(x), x_0) \rightarrow (\text{ev}, \pi)Open(pp,C,P(x),x0)→(ev,π) takes the public parameters pp\text{pp}pp, the commitment CCC, the polynomial P(x)P(x)P(x), and a point x0...
Commit: The commitment algorithm Commit(pp,P(x))→C\text{Commit}(\text{pp}, P(x)) \rightarrow CCommit(pp,P(x))→C takes the public parameters pp\text{pp}pp and the polynomial P(x)P(x)P(x), and outputs a commitment CCC.Commit:承诺算法 Commit(pp,P(x))→C\text{Commit}(\tex...
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Commit: A commitment algorithm that takes a polynomial and outputs a commitment. 提交:采用多项式并输出承诺的提交算法。 Open: An opening algorithm that reveals an evaluation at a specific point along with a proof. 开放:一种开放算法,揭示特定点的评估以及证明。
The runtime will now (in the worst case) be 2T. I can double the amount of work the algorithm does just by adding one more bit! An algorithm runs inpseudopolynomial timeif the runtime is some polynomialin the numeric value of the input, rather than in the number of bits required to...
However, solving a problem in exponential time is not fast enough. No polynomial time algorithm has been developed to solve the factoring problem, despite many years of research. Clearly there are examples of N for which this is very easy to solve, for example whenever N is even. Therefore,...
If a problem is in non-deterministic polynomial time, the non-deterministic Turing machine can first guess at the solution, and then run a verifiable algorithm that will confirm whether or not that guess was correct. Verifier-based definition or machine definition programs will in essence test the...
Polynomial time emerged as a way to talk about feasibility of algorithm work and development. If a problem is in non-deterministic polynomial time, the non-deterministic Turing machine can first guess at the solution, and then run a verifiable algorithm that will confirm whether or not that ...
Section 6 presents what is probably the most important theorem ever proved in matroid theory, a decomposition theorem that not only describes the structure of a fundamental class of matroids but also implies a polynomial-time algorithm for a basic problem in combinatorial optimization. Section 7 ...