We show that Nechiporuk’s method [14] for proving lower bound for Boolean formulas can be extended to the quantum case. This leads to an Ω(n2/ log n) lower bound for quantum formulas computing an explicit function. The only known previous explicit lower bound for quantum formulas [15] states that the majority function does not have a linear–size quantum formula.

Recall the online learning model we discussed in the previous lecture: N = # experts For t = 1, 2, . . . , T rounds: 1) each expert i, 1 ≤ i ≤ N , makes a prediction ξi ∈ {0, 1} 2) learner makes a prediction ŷ ∈ {0, 1} 3) observe outcome y ∈ {0, 1} (a mistake happens if ŷ 6= y) With this framework in hand, we investigated a particular algorithm, Weighted Majority Algorithm (WMA), as follows: N ...

Quantum-dot cellular automata (QCA) technology is believed to be a good alternative CMOS technology. This nanoscale can provide platform for design and implementation of high performance power efficient logic circuits. However, the fabrication QCA circuits susceptible faults appearing in this form missing cells, additional rotated cells displaced cells. Over years, several solutions have been p...

This paper studies coalition formation, payoff division and expected payoffs in a ”divide the dollar by majority rule” game with random proposers. A power index is called self-confirming if it can be obtained as an equilibrium of the game using the index itself as probability vector. Unlike the Shapley value and other commonly used power indices, the nucleolus has this property. The proof uses ...

We develop a general concept of majority rule for finitely many choice alternatives that is consistent with arbitrary binary preference relations, real-valued utility functions, probability distributions over binary preference relations, and random utility representations. The underlying framework is applicable to virtually any type of choice, rating, or ranking data, not just the linear orders...

Two new low-power, and high-performance 1bit Full Adder cells are proposed in this paper. These cells are based on low-power XOR/XNOR circuit and Majority-not gate. Majority-not gate, which produces Cout (Output Carry), is implemented with an efficient method, using input capacitors and a static CMOS inverter. This kind of implementation benefits from low power consumption, a high degree of reg...

In recent years, memory cells have become more susceptible to soft errors. This must be protected with effective error correction codes. Majority logic decodable codes are suitable for memory applications because of their capability to correct large number of errors. Conversely, they increase the average latency of the decoding process because it depends upon the code size that impacts memory p...

The fundamental logical element of a quantum-dot cellular automata (QCA) circuit is majority voter gate (MV). The efficiency of a QCA circuit is depends on the efficiency of the MV. This paper presents an efficient single layer five-input majority voter gate (MV5). The structure of proposed MV5 is very simple and easy to implement in any logical circuit. This proposed MV5 reduce number of cells...