31 citations · 317 across the 62 of their papers we have counts for
13 papers · 1 filter
Partial clones containing all Boolean monotone self-dual partial functions
Miguel Couceiro, Lucien Haddad, Ivo G. Rosenberg
The study of partial clones on was initiated by R. V. Freivald. In his fundamental paper published in 1966, Freivald showed, among other things, that the set…
Hereditarily rigid relations
Miguel Couceiro, Lucien Haddad, Maurice Pouzet +1
An -ary relation $\r$ on a finite set is said to be \emph{hereditarily rigid} if the unary partial functions on that preserve $\r$ are the subfunctions of the identity m…
Set-reconstructibility of Post classes
Miguel Couceiro, Erkko Lehtonen, Karsten Schölzel
The clones of Boolean functions are classified in regard to set-reconstructibility via a strong dichotomy result: the clones containing only affine functions, conjunctions, disjunc…
Hypomorphic Sperner systems and nonreconstructible functions
Miguel Couceiro, Erkko Lehtonen, Karsten Schölzel
A reconstruction problem is formulated for Sperner systems, and infinite families of nonreconstructible Sperner systems are presented. This has an application to a reconstruction p…
Additive decomposability of functions over abelian groups
Miguel Couceiro, Erkko Lehtonen, Tamás Waldhauser
Abelian groups are classified by the existence of certain additive decompositions of group-valued functions of several variables with arity gap 2.
On the lattice of equational classes of Boolean functions and its closed intervals
Miguel Couceiro
Let A be a finite set with at least two elements. The composition of two classes I and J of operations on A, is defined as the set of all compositions of functions in I with functi…
Decompositions of functions based on arity gap
Miguel Couceiro, Erkko Lehtonen, Tamás Waldhauser
We study the arity gap of functions of several variables defined on an arbitrary set A and valued in another set B. The arity gap of such a function is the minimum decrease in the…
Join-irreducible Boolean functions
Moncef Bouaziz, Miguel Couceiro, Maurice Pouzet
This paper is a contribution to the study of a quasi-order on the set of Boolean functions, the \emph{simple minor} quasi-order. We look at the join-irreducible members of the…
Function classes and relational constraints stable under compositions with clones
Miguel Couceiro, Stephan Foldes
The general Galois theory for functions and relational constraints over arbitrary sets described in the authors' previous paper is refined by imposing algebraic conditions on relat…
Irreducible Boolean Functions
Moncef Bouaziz, Miguel Couceiro, Maurice Pouzet
This paper is a contribution to the study of a quasi-order on the set of Boolean functions, the \emph{simple minor} quasi-order. We look at the join-irreducible members of the…
Generalizations of Swierczkowski's lemma and the arity gap of finite functions
Miguel Couceiro, Erkko Lehtonen
Swierczkowski's Lemma - as it is usually formulated - asserts that if f is an at least quaternary operation on a finite set A and every operation obtained from f by identifying a p…
On the effect of variable identification on the essential arity of functions
Miguel Couceiro, Erkko Lehtonen
We show that every function of several variables on a finite set of k elements with n>k essential variables has a variable identification minor with at least n-k essential variable…
On a quasi-ordering on Boolean functions
Miguel Couceiro, Maurice Pouzet
It was proved few years ago that classes of Boolean functions definable by means of functional equations \cite{EFHH}, or equivalently, by means of relational constraints \cite{Pi2}…