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While previous works describe other practical acceleration techniques for some of the mentioned problems [ 14, 25, 28, 32- 38], Valiant's technique, along with the Four Russians technique [ 28, 30, 31], are the only two techniques which currently allow to reduce the theoretical asymptotic worst case running times of the standard algorithms, without compromising the correctness of the computations.
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"The consensus committee then verifies the correctness of the computation results from the computation committee.
We use different mathematical and cryptographic methods to enable efficient verification of the correctness of the computation results.
By having the computation committee working in parallel with the consensus committee only needing to verify the correctness of the computation creates an easier path to scalability.
An accurate computation of the value requires the system to spend a certain amount of energy for guaranteeing the correctness of the computation.
The argumentation for the correctness of the computation of S w, v, c w) follows analogously.
The correctness of the computation conducted lines 10-13 in the case where l - j < k - i is shown similarly.
The proof of Theorem 1 appears in Appendix "Correctness of the recursive computation".
A simple script from α to β w is non-reducing (as shown in Section "Correctness of the recursive computation").
This section proves Theorem 1, thus asserting the correctness of the recursive computation for the EDDC problem given in Section "The recurrence formula".
Since the proof of correctness of these recursive formulas is similar to previous ones, we defer it to Appendix "Correctness of the recursive computation".
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