These lecture notes will develop the method of binary decision diagrams – a technique for representing Boolean functions – from automata theory. We include a compact presentation of automata theory required for the purpose, and indicate applications.

A reduct is a subset of attributes that are jointly sufficient and individually necessary for preserving a particular property of a given information system. The existing reduct approaches under soft set theory are still based on Boolean-valued information system. However, in the real applications, the data usually contain non-Boolean values. In this paper, an alternative approach for attribute...

Abstraction of digital MOS circuits as switch-level networks has proven very useful for VLSI automation. Symbolic analysis of switch-level networks by representing the signal at the gate of a MOS transistor as a Boolean variable has been shown to be efficient for verification in terms of functionality and timing. For this work, in addition to expressing the signal at the gate of MOS transistors...

We onsider a fundamental problem in omputational learning theory: learning an arbitrary Boolean fun tion that depends on an unknown set of k out of n Boolean variables. We give an algorithm for learning su h fun tions from uniform random examples that runs in time roughly (n k ) ! !+1 ; where ! < 2:376 is the matrix multipli ation exponent. We thus obtain the rst polynomial fa tor improvement o...

0. Notation. The basic notation for Boolean algebras is the standard one (for instance, see [l]). Throughout this paper, the letter O will denote the two-element Boolean algebra; whenever a topology is assumed to be defined on 0, then this topology is the discrete one. If 73 is a Boolean algebra, then a valuation of B is a homomorphism from 73 onto 0. We make precise the terminology we shall be...

We generalize to universal algebra concepts originating from λ-calculus and programming to prove a new result on the lattice λT of λ-theories, and a general theorem of pure universal algebra which can be seen as a meta version of the Stone Representation Theorem. In this paper we introduce the class of Church algebras (which includes all Boolean algebras, combinatory algebras, rings with unit a...

We consider a fundamental problem in computational learning theory: learning an arbitrary Boolean function that depends on an unknown set of k out of n Boolean variables. We give an algorithm for learning such functions from uniform random examples that runs in time roughly ðnÞ o oþ1; where oo2:376 is the matrix multiplication exponent. We thus obtain the first-polynomial factor improvement on ...

The higher order nonlinearity of a Boolean function is a cryptographic criterion, which play a role against attacks on stream and block ciphers. Also it play a role in coding theory, since it is related to the covering radii of Reed-Muller codes. In this paper, we study the lower bounds of second-order nonlinearities of a class of cubic Boolean functions of the form with and ∈ ′ and some classe...

The orthogonal conjunctive normal form of a Boolean function is a conjunctive normal form in which any two clauses contain at least a pair of complementary literals. Orthogonal disjunctive normal form is defined similarly. Orthogonalization is the process of transforming the normal form of a Boolean function to orthogonal normal form. The problem is of great relevance in several applications, f...

These notes present a compact and self contained development of the theory of iterated forcing with a focus on semiproperness and revised countable support iterations. We shall pursue the approach to iterated forcing devised by Donder and Fuchs in [4], thus we shall present iterated forcing by means of directed system of complete and injective homomorphisms of complete boolean algebras. A guidi...