Boolean network models have gained popularity in computational systems biology over the last dozen years. Many of these networks use canalizing Boolean functions, which has led to increased interest in the study of these functions. The canalizing depth of a function describes how many canalizing variables can be recursively “picked off”, until a non-canalizing function remains. In this paper, w...

In this paper the problem of decomposition, mapping and minimization of multi-output boolean functions is discussed. First the mathematical formulation for single-output boolean functions is presented and then it is extended to multi-output functions. The proposed formulations use function decompositions, ETDDs (EXOR ternary decision diagrams) and multi-valued logic.

The expressiveness of Boolean Algebras is significantly extended by the Boolean Differential Calculus (BDC). The additionally defined differentials of Boolean variables, differentials and further differential operators of Boolean functions as well as several derivative operations of Boolean functions allow to model changes of function values together with changes of the values of variables and ...

We show that Nechiporuk’s method [26] for proving lower bounds for Boolean formulas can be extended to the quantum case. This leads to an Ω(n/ log n) lower bound for quantum formulas computing an explicit function. The only known previous explicit lower bound for quantum formulas [27] states that the majority function does not have a linear–size quantum formula. We also show that quantum formul...

Extended Boolean retrieval (EBR) models were proposed nearly three decades ago, but have had little practical impact, despite their significant advantages compared to either ranked keyword or pure Boolean retrieval. In particular, EBR models produce meaningful rankings; their query model allows the representation of complex concepts in an and–or format; and they are scrutable, in that the score...

Information retrieval can be achieved through computerized processes by generating a list of relevant responses to a query. The document processor, matching function and query analyzer are the main components of an information retrieval system. Document retrieval system is fundamentally based on: Boolean, vector-space, probabilistic, and language models. In this paper, a new methodology for mat...

Information retrieval can be achieved through computerized processes by generating a list of relevant responses to a query. The document processor, matching function and query analyzer are the main components of an information retrieval system. Document retrieval system is fundamentally based on: Boolean, vector-space, probabilistic, and language models. In this paper, a new methodology for mat...

This is Part 6 of a tutorial series on Term Vector Theory. The Extended Boolean Model is discussed. By varying the model p-norm parameter, from p = 1 to p = , we can vary its ranking behavior from that of a vector spacelike to that of a strict Boolean-like.