Skew lattices and binary operations on functions

Derivative Operations for Lattices of Boolean Functions

This paper explores derivative operations of the Boolean differential calculus for lattices of Boolean functions. Such operations are needed to design circuits with short delay and low power consumption [3] as well as to calculate minimal complete sets of fitting test patterns [4]. It will be shown that each derivative operation of a lattice of Boolean functions creates again a lattice of Boole...

On Pseudorandom Binary Lattices

Cancellation in Skew Lattices

Distributive lattices are well known to be precisely those lattices that possess cancellation: x ∨ y = x ∨ z and x ∧ y = x ∧ z imply y = z. Cancellation, in turn, occurs whenever a lattice has neither of the 5-element lattices M3 or N5 as sublattices. In this paper we examine cancellation in skew lattices, where the involved objects are in many ways lattice-like, but the operations ∧ and ∨ no l...

Categorical Skew Lattices

Categorical skew lattices are a variety of skew lattices on which the natural partial order is especially well behaved. While most skew lattices of interest are categorical, not all are. They are characterized by a countable family of forbidden subalgebras. We also consider the subclass of strictly categorical skew lattices.

Generalized Lattices of Boolean Functions Utilized for Derivative Operations

This paper explores lattices of Boolean functions which are built by derivative operations of the Boolean Differential Calculus [2], [8], [9]. Such operations are needed to design circuits with short delay and low power consumption [11] as well as to calculate minimal complete sets of fitting test patterns [12]. It will be shown that each derivative operation of a lattice of Boolean functions c...