Flexibility in selecting the Boolean functions to implement a digital circuit has various forms which have been studied in the literature such as don't care conditions, Boolean relations, and synchronous recurrence equations. Each of these represents a particular degree of exibility that may be given in the description, inherent in the current representation, or derived from the surrounding env...

Boolean networks form a class of disordered dynamical systems that have been studied in physics owing to their relationships with disordered systems in statistical mechanics and in biology as models of genetic regulatory networks. Recently they have been generalized to probabilistic Boolean networks (PBNs) to facilitate the incorporation of uncertainty in the model and to represent cellular con...

Despite advancements in specifying 3D internal microstructure of reservoir rocks, identifying some sensitive phenomenons are still problematic particularly due to image resolution limitation. Discretization study on such CT-scan data always has encountered with such conflicts that the original data do not fully describe the real porous media. As an alternative attractive approach, one can recon...

We show that while the length ω iterated ultrapower by a normal ultrafilter is a Boolean ultrapower by the Boolean algebra of Př́ıkrý forcing, it is consistent that no iteration of length greater than ω (of the same ultrafilter and its images) is a Boolean ultrapower. For longer iterations, where different ultrafilters are used, this is possible, though, and we give Magidor forcing and a general...

Boolean Networks (BNs) are established models to qualitatively describe biological systems. The analysis of BNs might be infeasible for medium large due the state-space explosion problem. We propose a novel reduction technique called Backward Equivalence (BBE), which preserves some properties interest BNs. In particular, reduced provide compact representation by grouping variables that, if init...

Basic results in combinatorial mathematics provide the foundation for a theory and calculus for reasoning about sequential behavior. A key concept of the theory is a generalization of Boolean implicant in which one now deals with statements of the form: A sequence of Boolean expressions α is an implicant of a set of sequences of Boolean expressions A This notion of a generalized implicant takes...