In multi-component, discrete systems, such as Boolean networks and cellular automata, the scheme of updating of the individual elements plays a crucial role in determining their dynamic properties and their suitability as models of complex phenomena. Many interesting properties of these systems rely heavily on the use of synchronous updating of the individual elements. Considerations of parsimo...

Deterministic Boolean networks have been used as models of gene regulation and other biological networks. One key element in these models is the update schedule, which indicates the order in which states are to be updated. We study the robustness of the dynamical behavior of a Boolean network with respect to different update schedules (synchronous, block-sequential, sequential), which can provi...

Boolean functions and vectorial are the most important nonlinear components of stream ciphers. They should satisfy several criteria such as high nonlinearity, proper resiliency so on to guarantee security whole system. However, there some constraints among criteria, how achieve a trade-off between them is an issue. In this paper, possessing simple algebraic normal form with special Walsh spectr...

A simplicial poset P (also called a boolean poset and a poset of boolean type) is a finite poset with a smallest element 0̂ such that every interval [0̂, y] for y ∈ P is a boolean algebra, i.e., [0̂, y] is isomorphic to the set of all subsets of a finite set, ordered by inclusion. The set of all faces of a (finite) simplicial complex with empty set added forms a simplicial poset ordered by inclusi...

It is shown that the four element Boolean algebra can be embedded in the recursively enumerable truth-table degrees with least and greatest elements preserved. Corresponding results for other lattices and other reducibilites are also discussed. For sets A, B ç co, we say that A is a truth-table (tt) reducible to B if there exists an effective procedure for reducing any question of the form "m e...