Extended Abstract In this Note I prove a representation theorem for Peirce algebras introduced in Brink, Britz and Schmidt (1994b, 1994a). I show that the class of full Peirce algebras is characterised by the class of complete and atomic Peirce algebras in which the set of relational atoms is restricted by two conditions. One requires simplicity. The other requires that each relational element ...

The Facebook discussion with Stephen King about Stone spaces led to a highly interesting development of ideas concerning Boolean, algebras, Stone spaces, and p-adic physics. I have discussed these ideas already earlier but the improved understanding of the notion of Stone space helped to make the ideas more concrete. The basic ideas are briefly summarized. p-adic integers/numbers correspond to ...

The (fast) algebraic immunity, including (standard) algebraic immunity and the resistance against fast algebraic attacks, has been considered as an important cryptographic property for Boolean functions used in stream ciphers. This paper is on the determination of the (fast) algebraic immunity of a special class of Boolean functions, called Boolean power functions. An n-variable Boolean power f...

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 ...

Da Ré and Szmuc argue that while there is a symmetry between ‘infectious’ ‘immune’ logics, this fails w.r.t. extending an algebra with immune or infectious element. In paper, I show the also defining new logical operation from given set of primitive (Boolean) operations. use case material conditional to illustrate point.

This article uses a recently presented abstract, tunable Boolean regulatory network model to further explore aspects of mobile DNA, such as transposons. The significant role of mobile DNA in the evolution of natural systems is becoming increasingly clear. This article shows how dynamically controlling network node connectivity and function via transposon-inspired mechanisms can be selected for ...

For posets P and Q, extremal saturation problems about weak strong P-free subposets of Q have been studied mostly in the case is Boolean poset Qn, all subsets an n-element set ordered by inclusion. In this paper, we study some instances problem with being grid, its connections to forbidden submatrix problem.

For set-theoretical notation we follow [3]. We follow [2] for Boolean algebraic notation, and Monk [5] for more specialized notation concerning cardinal functions on Boolean algebras. Fr(κ) is the free Boolean algebra on κ generators. A is the completion of A. If L is a linear order, then Intalg(L) is the interval algebra over L (perhaps after adjoining a first element to L). Any element x of I...

Let L1 be a finite simple sloop of cardinality n or the 8-element sloop. In this paper, we construct a subdirectly irreducible (monolithic) sloop L = 2⊗αL1 of cardinality 2n, for each n ≥ 8, with n ≡ 2 or 4 (mod 6), in which each proper homomorphic image is a Boolean sloop. Quackenbush [12] has proved that the variety V (L1) generated by a finite simple planar sloop L1 covers the smallest nontr...

We prove that a Boolean function on Sn whose Fourier transform is highly concentrated on the first two irreducible representations of Sn, is close to dictator, a function which is determined by the image or pre-image of a single element. As a corollary we get a stability result concerning extremal isoperimetric sets in the Cayley graph of transpositions on Sn. Our proof works in the case where ...