Sentence examples for this problem was proven from inspiring English sources

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

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

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).

Regular solvability of the Problem B with continuous gluing conditions ( α = 1, β = 0 ) have been proved, for the first time, in [27], and strong solvability of this problem was proved in the work [28].

This problem was proved by Gomez et al. [ 57], whose study confirms a correlation between drug addiction and an increase of abnormal occluso-muscle function.

This problem is proven to be closely related with the 2-hop labeling scheme [9].

As this problem is proven to be NP-hard, a multi-phase approach is developed to solve it.

Furthermore, this problem is proven to be NP-hard, which leads us to developing an effective approximation by heuristically restricting the search space (i.e., TRCRea).

But solving this problem is proving relatively straightforward, if time consuming and expensive.

The solvability of this problem is proved.

The theorem on the necessary and sufficient conditions to solve this problem is proved.