Pivotal decomposition schemes inducing clones of operations

Clones with Nullary Operations

This article discusses clones with nullary operations and the corresponding relational clones, both defined on arbitrary sets. By means of two pairs of kernel and closure operators, the relationship between such clones and clones in the traditional sense, i.e. without nullary operations, is investigated, and in particular the latter type of clones is located in the lattice of all clones. Finall...

Are Decomposition Slices Clones?

When computing program slices on all variables in a system, we observed that many of these slices are the same. This leads to the question: Are we looking at software clones? We discuss the genesis of this phenomena and present some of the data observations that led to the question. The answer to our query is not immediately clear. We end by presenting arguments both pro and con. Supporting the...

On Some Clones of Compatible Operations

In [5], new results on affine complete algebras are obtained using the formalism of generalized metric spaces introduced by Jawhari, Misane and Pouzet [3]. In this paper we focus our attention to the clones of compatible operations obtained by the mean of nonexpansive functions defined on a generalized metric space. We hence prove new results on relations and primal algebras. We apply the notio...

Lifting Measures to Inducing Schemes

In this paper we study the liftability property for piecewise continuous maps of compact metric spaces, which admit inducing schemes in the sense of [PS05, PS07]. We show that under some natural assumptions on the inducing schemes – which hold for many known examples – any invariant ergodic Borel probability measure of sufficiently large entropy can be lifted to the tower associated with the in...

A note on clones with nullary operations