1. Overview This paper talks about that monotone circuit is P-Complete. Decision problem that include P-Complete is mapping that classify input with a similar property. Therefore equivalence relation of input value is important for computation. But monotone circuit cannot compute the equivalence relation of the value because monotone circuit can compute only monotone function. Therefore, I make...

In the last few years there has been renewed interest in the classical control problem of de Finetti [10] for the case that underlying source of randomness is a spectrally negative Lévy process. In particular a significant step forward is made in [25] where it is shown that a natural and very general condition on the underlying Lévy process which allows one to proceed with the analysis of the a...

The problem of maximizing a constrained monotone set function has many practical applications and generalizes many combinatorial problems such as k-Coverage, Max-SAT, Set Packing, Maximum Independent Set and Welfare Maximization. Unfortunately, it is generally not possible to maximize a monotone set function up to an acceptable approximation ratio, even subject to simple constraints. One highly...

We characterize the size of monotone span programs computing certain “structured” boolean functions by the Nullstellensatz degree of a related unsatisfiable Boolean formula. This yields the first exponential lower bounds for monotone span programs over arbitrary fields, the first exponential separations between monotone span programs over fields of different characteristic, and the first expone...

Given a probability measure over a state space, a partial collection (sub-σalgebra) of events whose probabilities are known, induces a capacity over the collection of all possible events. The induced capacity of an event F is the probability of the maximal (with respect to inclusion) event contained in F whose probability is known. The Choquet integral with respect to the induced capacity coinc...

We investigate the following extendability problem for systems, for which the available information is given by a monotone set mapping M on the field CT of measurable cylinders of a product ample space (XT ,RT ): given that M is invariant under a RT −RT measurable transformation H of XT , i.e. M(H−1(B)) = M(B) for all B ∈ CT , is it possible to find H-invariant monotone extensions of M to the p...

Consensus based approaches provide a way to drive group decisions which are more accepted and appreciated by decision makers. Different consensus approaches and methodologies have been proposed to conduct these processes successfully, but there still remain some aspects that must be further studied, such as the use and effects of different aggregation operators to measure consensus in the group...

We establish the characterisations of classes bounded linear operators from generalised Hahn sequence space hd, where d is an unbounded monotone increasing positive real numbers, into spaces w0, w and w? sequences that are strongly summable to zero, by Ces?ro method order one. Furthermore, we prove estimates for Hausdorff measure noncompactness hd w, identities use these results characterise co...

We analyze decision-makers who make stochastic choices from sets of lotteries. A random choice rule associates with each decision problem a probability measure over the feasible choices. A random utility is a probability measure over von Neumann-Morgenstern utility functions. We show that a random choice rule maximizes some random utility if and only if it is mixture continuous, monotone (the p...

Consider two orthogonal closed chains on a cylinder. The chains are monotone with respect to the angle Θ. We wish to rigidly move one chain so that the total area between the two chains is minimized. This is a geometric measure of similarity between two repeating melodies proposed by Ó Maid́ın. We present an O(n) time algorithm to compute this measure if Θ is not allowed to vary, and an O(n log ...