This paper proposes an algorithm for deciding consistency of systems of Boolean equations in several variables with co-efficients in the two element Boolean algebra B0 = {0, 1} and find all satisfying assignments. The algorithm is based on the application of a well known generalized Boole-Shannon orthonormal (ON) expansion of Boolean functions. A necessary and sufficient consistency condition f...

A subset H f0; 1g n is a Hitting Set for a class R of boolean functions with n inputs if, for any function f 2 R such that Pr (f = 1) (where 2 (0; 1) is some xed value), there exists an element ~ h 2 H such that f (~ h) = 1. The eecient construction of Hitting Sets for non trivial classes of boolean functions is a fundamental problem in the theory of derandomization. Our paper presents a new me...

In this paper we study n-input m-output Boolean functions (abbr. (n,m)-functions) with high nonlinearity. First, we present a basic construction method for a balanced (n,m)-function based on a primitive element in GF (2m). With an iterative procedure, we improve some lower bounds of the maximum nonlinearity of balanced (n,m)-functions. The resulting bounds are larger than the maximum nonlineari...

A group is ^-separating if a Boolean power of the group has a unique Boolean algebra. It is proved that a finite subdirectly irreducible group is S-separating if and only if it is non-Abelian. Suppose B is a Boolean ring and G is a group. Let B[G] denote the group ring of G with coefficient ring B. The Boolean power G [B] is defined to be the set of those elements 2e,.g,. EB[G] such that (1) 2e...

Abstract A 2-dimension linguistic lattice implication algebra (2DL-LIA) can build a bridge between logical and fuzzy information. In this paper, the notion of Boolean element is proposed in 2DL-LIA some properties elements are discussed. Then derivations on 2DL-LIAs introduced related investigated. Moreover, it proves that be constructed by elements.

1. Introduction IT is well known that there are a number of sets of axioms for Boolean algebra. In this paper, I give a set of five independent axioms using conditioned disjunction as the ternary operation which is postulated. The ternary operation is most naturally defined on the set 2 n —this is done in §2. The theorem is stated in §3 together with a slight generalization of this result; the ...

Information retrieval on XML combines retrieval on content data (element and attribute values) with retrieval on structural data (element and attribute names). Standard query languages for XML such as XPath or XQuery support Boolean retrieval: a query result is a (possibly restructured) subset of XML elements or entire documents that satisfy the search conditions of the query. Such search condi...

We present the design of an autonomous time-delay Boolean network realized with readily available electronic components. Through simulations and experiments that account for the detailed nonlinear response of each circuit element, we demonstrate that a network with five Boolean nodes displays complex behavior. Furthermore, we show that the dynamics of two identical networks display near-instant...

A countable structure (with finite signature) is computable if its universe can be identified with ω in such a way as to make the relations and operations computable functions. In this thesis, I study which Boolean algebras and linear orders are computable. Making use of Ketonen invariants, I study the Boolean algebras of low Ketonen depth, both classically and effectively. Classically, I give ...

boolean Element::isConnectedTo(Element n); An implementation, with the same signature (i.e., name and input/output types), should be defined for all concrete classes that inherit from Element, namely for the classes ANode, CNode and Link. We define different implementations for Link and Node (i.e., for both ANode and CNode). Here is the implementation for the abstract class Node: boolean Node::...