Sentence examples for problem was proven from inspiring English sources

First the #P-completeness of this problem was proven.

The MSA problem was proven NP-Hard, thus requiring a high amount of memory and computing power.

In dimension n ≥ 3 and in the case of a compactly supported electric potential, uniqueness for the fixed energy scattering problem was proven in [135, 145, 159].

Since the considered optimization problem was proven NP-hard (Chern 1992) and Heuristic algorithms do not provide an assurance for optimization of the problem (Bashiri and Karimi 2012), therefore, meta-heuristic algorithms used to generate near optimal solutions.

Although this problem was proven to be NP-hard [ 58], several algorithms have been developed for its solution.

But Paul Nicholls admitted that the Lexus Chase winner's problem was proving difficult to diagnose – potentially a foot infection or a small pulled muscle – and has not yet given up hope.

Moreover, the uniqueness of solution and the Volterra property of the formulated problem was proved.

For some simple distributions of the similarities, the seed optimization problem was proved to be not NP-hard.

In the work [4] the existence of a solution global in time for the described problem was proved.

That this quadratic "speed-up" is also the optimal quantum "speed-up" possible for this problem was proved by Bennett, Bernstein, Brassard and Vazirani (1997).

In addition, the problem was proved to be NP-hard in general graphs [15], and remains so even when restricted to bipartite graphs [22].