Formulas for approximating pseudo-Boolean random variables

Formulas for approximating pseudo-Boolean random variables

We consider {0, 1}n as a sample space with a probability measure on it, thus making pseudo-Boolean functions into random variables. We then derive explicit formulas for approximating a pseudo-Boolean random variable by a linear function if the measure is permutation-invariant, and by a function of degree at most k if the measure is a product measure. These formulas generalize results due to Ham...

Transforms of pseudo-Boolean random variables

In most cases authors are permitted to post their version of the article (e.g. in Word or Tex form) to their personal website or institutional repository. Authors requiring further information regarding Elsevier's archiving and manuscript policies are encouraged to visit: a b s t r a c t As in earlier works, we consider {0, 1} n as a sample space with a probability measure on it, thus making ps...

Deciding CLU Logic Formulas via Boolean and Pseudo-Boolean Encodings

Random Formulas Have Frozen Variables

For a large number of random constraint satisfaction problems, such as random k-SAT and random graph and hypergraph coloring, we have very good estimates of the largest constraint density for which solutions exist. Yet, all known polynomial-time algorithms for these problems fail to find solutions even at much lower densities. To understand the origin of this gap one can study how the structure...

Variance Formulas for Trapezoidal Fuzzy Random Variables∗

The variance of fuzzy random variables often appears in fuzzy random programming problems. Based on the definition of the variance of a fuzzy random variable, this paper attempts to deduce several formulas for the variances of trapezoidal fuzzy random variables, in which the randomness is characterized by uniform distribution. Firstly, we give the moment formulas for trapezoidal fuzzy variables...