Replaceability and computational equivalence in finite distributive lattices
Meurig Beynon · Warwick Research Archive Portal (University of Warwick) · 1984
Notions of replaceability and computational equivalence are defined in an abstract algebraic setting, and investigated in detail for finite distributive lattices. It is shown that, when computing an element f of a finite distributive lattice D, the elements of D partition into classes of computationally equivalent elements, and define a quotient of D in which all intervals of the form [t/\f, t\/f] are boolean. This quotient is an abstract simplicial complex with respect to ordering by replaceability. Other results include generalisations and extensions of known theorems concerning replacement rules for monotone boolean networks.