On generalized circulants over a Boolean algebra

Powers of Circulants in Bottleneck Algebra

Consider the powers of a square matrix A of order n in bottleneck algebra, where addition and multiplication are replaced by the max and min operations. The powers are periodic, starting from a certain power AK . The smallest such K is called the exponent of A and the length of the period is called the index of A. Cechlárová has characterized the matrices of index 1. Here we consider the case w...

On Some Properties of the Max Algebra System Over Tensors

Recently we generalized the max algebra system to the class of nonnegative  tensors. In this paper we give some basic properties for the left (right) inverse, under the new system. The existence of order 2 left (right) inverse of tensors is characterized. Also we generalize the direct product of matrices to the direct product of tensors (of the same order, but may be different dimensions) and i...

Ternary Boolean Algebra

Boolean Algebra Approximations

Knight and Stob proved that every low4 Boolean algebra is 0-isomorphic to a computable one. Furthermore, for n = 1, 2, 3, 4, every lown Boolean algebra is 0-isomorphic to a computable one. We show that this is not true for n = 5: there is a low5 Boolean algebra that is not 0-isomorphic to any computable Boolean algebra. It is worth remarking that, because of the machinery developed, the proof u...

Free Boolean Algebra

This theory defines a type constructor representing the free Boolean algebra over a set of generators. Values of type (α)formula represent propositional formulas with uninterpreted variables from type α, ordered by implication. In addition to all the standard Boolean algebra operations, the library also provides a function for building homomorphisms to any other Boolean algebra type. 1 Free Boo...