23 марта на Межкафедральном семинаре «Теоретическая информатика и комбинаторика» в Актовом зале МФТИ в 18:30 Владимир Подольский прочтёт лекцию на английском языке «Computing Majority by Constant Depth Majority Circuits with Low Fan-in Gates». Это заседание проходит в рамках совместного семинара ФИВТ МФТИ и ФКН ВШЭ.
Abstract
We study the following computational problem: for which values of k, the majority of n bits MAJn can be computed with a depth two formula whose each gate computes a majority function of at most k bits? The corresponding computational model is denoted by MAJk ○ MAJk. We observe that the minimum value of k for which there exists a MAJk ○ MAJk circuit that has high correlation with the majority of n bits is equal to ϴ(n1/2). We then show that for a randomized MAJk ○ MAJk circuit computing the majority of n input bits with high probability for every input, the minimum value of k is equal to n2=3+o(1). We show a worst case lower bound: if a MAJk ○ MAJk circuit computes the majority of n bits correctly on all inputs, then k ≥ n13=19+o(1). This lower bound exceeds the optimal value for randomized circuits and thus is unreachable for pure randomized techniques. For depth 3 circuits we show that a circuit with k = O(n2/3) can compute MAJn correctly on all inputs.
The talk is based on joint results with Alexander Kulikov.
The talk is based on joint results with Alexander Kulikov.
