Sentence examples for exists an efficient from inspiring English sources

In general, suppose that there exists an efficient mechanism with an "ex post" equilibrium.

In particular, whenever the UCEM property holds, there exists an efficient (i.e., polynomial-time) randomized algorithm.

Then by a version of the revelation principle there exists an efficient direct mechanism in which truth-telling is an "ex post" equilibrium.

In this paper, we provide a proof that the problem is indeed NP-hard, so it is not likely that there exists an efficient algorithm that solves the problem optimally.

Computability: there exists an efficient algorithm to calculate e u,v), for all u,v∈G.  .

(4) Gap Diffie-Hellman (GDH) group: If there exists an efficient PPT algorithm to solve the DDH problem and no PPT algorithm to solve the CDH problem, then G 1, a prime group, is defined as a GDH group.

CDH assumption: There does not exist an efficient PPT (probabilistic polynomial time) algorithm in G 1 to solve CDH problem.

(6) q-SDH assumption: There does not exist an efficient PPT algorithm to solve q-SDH problem.

It is not difficult to see that if there existed an efficient algorithm for deciding \(\sc{FACTORIZATION}\), then there would also exist an efficient algorithm for determining prime factorizations.[3] It is also easy to see that the function taking \(x\) to its prime factorization is effectively computable in the traditional sense of computability theory.

(1) Computational Diffie-Hellman (CDH) problem: Sample: (P ,a, P b Pfor some (a,b in Z_{q}^) Output: abP   (2) CDH assumption: There does not exist an efficient PPT (probabilistic polynomial time) algorithm in G 1 to solve CDH problem.

To date, there does not exist an efficient heterologous expression system to cover entire SM clusters (30 – 80 kb) in a single cloning step.