In this paper we propose several efficient algorithms for assessing the resistance of Boolean functions against algebraic and fast algebraic attacks when implemented in LFSR-based stream ciphers. An algorithm is described which permits to compute the algebraic immunity d of a Boolean function with n variables in O(D) operations, for D ≈ ` n d ́ , rather than in O(D) operations necessary in all p...

The Causally Dynamic Hybrid Bond Graph is extended to the case of modeswitching behaviour. Mode-switching ‘trees’ of switches and elements are historically used by bond graph practitioners to represent elements with piecewise-continuous functions. This case is defined as ‘parametric switching’ for the purposes of the hybrid bond graph, since the switching is internal to the element, as opposed ...

This paper presents an algorithm for extract­ ing propositions from trained neural networks. The algorithm is a decompositional approach which can be applied to any neural network whose output function is monotone such as sig­ moid function. Therefore, the algorithm can be applied to multi-layer neural networks, re­ current neural networks and so on. The algorithm does not depend on training me...

In this paper we give new extremal bounds on polynomial threshold function (PTF) representations of Boolean functions. Our results include the following: • Almost every Boolean function has PTF degree at most n2 + O( √ n log n). Together with results of Anthony and Alon, this establishes a conjecture of Wang and Williams [32] and Aspnes, Beigel, Furst, and Rudich [4] up to lower order terms. • ...

In this paper the concept of an $Omega$- Almost Boolean ring is introduced and illistrated how a sheaf of algebras can be constructed from an $Omega$- Almost Boolean ring over a locally Boolean space.

Every Boolean function is uniquely defined by a polynomial modulo 2. The degree of a Boolean function is the degree of its defining polynomial. In cryptography, the Boolean functions of fixed degree played important role, for example, 1 or 2 degrees. Therefore, in finding algorithms that recognize properties of Boolean functions polynomials by their values vectors, it makes sense consider only ...

This paper presents various versions of a tautology checking algorithm that is related both to St̊almarck’s algorithm and the mechanism described by Kunz and Stoffel in Reasoning in Boolean Networks[KS97]. The algorithm uses as its central data structure the conjunction of a set of terms, with each term being a relation over a small number of variables. In St̊almarck’s algorithm the relation is l...

Evidence-based medicine seeks to base clinical decisions on the best currently available scientific evidence and is becoming accepted practice. A key role is played by systematic reviews, which synthesize the biomedical literature and rely on different information retrieval methods to identify a comprehensive set of relevant studies. With Boolean retrieval, the primary retrieval method in this ...

This paper reports a study that has established the possibility of improving effectiveness method figurative transformations in order to minimize symmetrical Boolean functions main and polynomial bases. Prospective reserves analytical were identified, such as simplification function conjuncterms using created equivalent based on inserting same followed by operation super-gluing variables. The w...