The validity of majority rule in an election with but two candidates— and so also of Condorcet consistency—is challenged. Axioms based on evaluating candidates—paralleling those of K. O. May characterizing majority rule for two candidates based on comparing candidates—lead to another method, majority judgment, that is unique in agreeing with the majority rule on pairs of “polarized” candidates....

The notion of a meander is introduced and studied. Roughly speaking, a meander is a sequence of integers (drawn from the set N= {I, 2, . . . . n}) that wanders back and forth between various subsets of N a lot. Using Ramsey theoretic proof techniques we obtain sharp lower bounds on the minimum length of meanders that achieve various levels of wandering. We then apply these bounds to improve exi...

Proof: We will think of the random circuits we are going to construct as built exclusively of Maj3 gates, that is, gates with fan-in three and unbounded fan-out, which compute the majority function on their three inputs. Because each of these gates can be constructed from four binary AND, OR gates (exercise!), this simplification does not affect the asymptotic size and depth of the circuit. The...

This paper gives the first separation between the power of formulas and circuits of equal depth in the AC[⊕] basis (unbounded fan-in AND, OR, NOT and MOD2 gates). We show, for all d(n) ≤ O( logn log logn ), that there exist polynomial-size depth-d circuits that are not equivalent to depth-d formulas of size n (moreover, this is optimal in that n cannot be improved to n). This result is obtained...

We study Boolean functions of an arbitrary number of input variables that can be realized by simple iterative constructions based on constant-size primitives. This restricted type of construction needs little global coordination or control and thus is a candidate for neurally feasible computation. Valiant’s construction of a majority function can be realized in this manner and, as we show, can ...

A new technique for implementation of morphological edge detectors, including median prefiltering is presented in this paper. The proposed technique uses a bit-serial algorithm based on the majority gate. Several morphological edge detectors are studied and experimental results are also presented.

In this paper we present a 1 bit Full Adder Cell. It was implemented with lesser number of transistors and lesser power consumption compared to the existing implementations of the Full Adder. Simulations are carried for supply voltages of 1.2v, 0.8v in HSPICE at 0.18μmCMOS technology. Proposed Full Adder results show that there was a reduction of power consumption and efficient in area. Area wa...

We consider the non-adaptive bit-probe complexity of the set membership problem, where a set S of size at most n from a universe of size m is to be represented as a short bit vector in order to answer membership queries of the form “Is x in S?” by non-adaptively probing the bit vector at t places. Let sN (m,n, t) be the minimum number of bits of storage needed for such a scheme. Buhrman, Milter...

This paper considers the problem of finding a meaningful template function that represents the common pattern of a sample of curves. To address this issue, a novel algorithm based on a robust version of the isometric featuring mapping (Isomap) algorithm is developed. Assuming that the functional data lie on an intrinsically low-dimensional smooth manifold with unknown underlying structure, we p...

This paper gives the first separation between the power of formulas and circuits of equal depth in the AC0[⊕] basis (unbounded fan-in AND, OR, NOT and MOD2 gates). We show, for all d(n) ≤ O( logn log logn ), that there exist polynomial-size depth-d circuits that are not equivalent to depth-d formulas of size no(d) (moreover, this is optimal in that no(d) cannot be improved to nO(d)). This resul...