This paper studies a prominent class of recursively-defined combinatorial functions, namely, the binomial and multinomial coefficients and probabilities. The paper reviews the basic notions and mathematical definitions of these four functions. Subsequently, it characterizes each...
Open access
Research Article10.9734/JAMCS/2018/42137
Diagnostic testing concerning categorical or dichotomized variables is ubiquitous in many fields including, in particular, the field of clinical or epidemiological testing. Typically, results are aggregated in two-by-two contingency-table format, from which a surprisingly huge nu...
Open access
Research Article10.9734/JAMCS/2018/39367
In standard problems of digital circuit design, a switching function (two-valued Boolean function) is specified declaratively as a (usually incomplete) asserted relation R(X,Z), or equivalently as an equation R(X,Z) = 1, where X and Z are inputs and outputs, respectively. To obta...
Open access
Research Article10.9734/JAMCS/2018/39285
Any system of ‘big’ Boolean equations can be reduced to a single Boolean equation {g(Z) = 1} . We propose a novel method for producing a general parametric solution for such a Boolean equation without attempting to minimize the number of parameters used, but instead using indepen...
Open access
Research Article10.9734/BJMCS/2017/33884
A prominent reliability model is that of the partially-redundant (k-out-of-n) system. We use algebraic as well as signal-flow-graph methods to explore and expose the AR algorithm for computing k-out-of-n reliability. We demonstrate that the AR algorithm is, in fact, both a recurs...
Open access
Research Article10.9734/BJMCS/2017/33642
This paper handles a prominent problem of project management, namely that of project scheduling under uncertainty. The paper models this problem as a vector-weighted voting system and expresses the indicator variable for the successful (on-time) completion of project activities a...
Open access
Research Article10.9734/BJMCS/2017/33161
This paper is a tutorial exposition on how to translate concepts of voting systems to the Boolean domain, and consequently on how to use Boolean tools in the computation of a prominent index of voting powers, viz., the Banzhaf voting index. We discuss Boolean representations for...
Open access
Research Article10.9734/BJMCS/2017/31191
A double-threshold system (DTS) is a system that is successful if and only if the weighted arithmetic sum of its successes/failures equals or exceeds a certain threshold T1 and is smaller than or equal to a certain threshold T2. Generally a DTS is neither symmetric nor coherent....
Open access
Research Article10.9734/BJMCS/2016/30264