Related papers: Clonoids of Boolean functions with a linear source…
Dualization of a monotone Boolean function on a finite lattice can be represented by transforming the set of its minimal 1 to the set of its maximal 0 values. In this paper we consider finite lattices given by ordered sets of their meet and…
A clone on a set X is a set of finitary operations on X which contains all projections and which is moreover closed under functional composition. Ordering all clones on X by inclusion, one obtains a complete algebraic lattice, called the…
The subsumption problem with respect to terminologies in the description logic ALC is EXPTIME-complete. We investigate the computational complexity of fragments of this problem by means of allowed Boolean operators. Hereto we make use of…
Looking at some monoids and (semi)rings (natural numbers, integers and p-adic integers), and more generally, residually finite algebras (in a strong sense), we prove the equivalence of two ways for a function on such an algebra to behave…
The purpose of this article is to investigate the combinatorial properties of the cross section lattice of a $J$-irreducible monoid associated with a semisimple algebraic group of one of the types $A_n$, $B_n$, or $C_n$. Our main tool is a…
We consider clones on countable sets. If such a clone has quasigroup operations, is locally closed and countable, then there is a function $f : \mathbb{N} \to \mathbb{N}$ such that the $n$-ary part of $C$ is equal to the $n$-ary part of…
The notion of commutation of operations in universal algebra leads to the concept of centralizer clone and gives rise to a well-known class of problems that we call centralizer problems, in which one seeks to determine whether a given set…
We propose a way to unify two approaches of non-cloning in quantum lambda-calculi: logical and algebraic linearities. The first approach is to forbid duplicating variables, while the second is to consider all lambda-terms as…
A clone of functions on a finite domain determines and is determined by its system of invariant relations (=predicates). When a clone is determined by a finite number of relations, we say that the clone is of finite degree. For each Minsky…
We prove that there is a lattice embedded from every countable distributive lattice into the Boolean algebra of computable subsets of $\mathbb{N}$. Along the way, we discuss all relevant results about lattices, Boolean algebras and…
We present a Galois theory connecting finitary operations with pairs of finitary relations one of which is contained in the other. The Galois closed sets on both sides are characterised as locally closed subuniverses of the full iterative…
If L is an order polynomially complete lattice, (that is: every monotone function from L^n to L is induced by a lattice-theoretic polynomial) then the cardinality of L is a strongly inaccessible cardinal. In particular, the existence of…
We investigate the complexity of the Boolean clone membership problem (CMP): given a set of Boolean functions $F$ and a Boolean function $f$, determine if $f$ is in the clone generated by $F$, i.e., if it can be expressed by a circuit with…
We show that that a certain class of semi-proper iterations does not add omega-sequences. As a result, starting from suitable large cardinals one can obtain a model in which the Continuum Hypothesis holds and every function from omega_1 to…
On an arbitrary meet-semilattice S with 0 we define an orthogonality relation and investigate the lattice Cl(S) of all subsets of S closed under this orthogonality. We show that if S is atomic then Cl(S) is a complete atomic Boolean…
Using Koszmider's strongly unbounded functions, we show the following consistency result: Suppose that $\kappa,\lambda$ are infinite cardinals such that $\kappa^{+++} \leq \lambda$, $\kappa^{<\kappa}=\kappa$ and $2^{\kappa}= \kappa^+$, and…
The concept of a clone is central to many branches of mathematics, such as universal algebra, algebraic logic, and lambda calculus. Abstractly a clone is a category with two objects such that one is a countably infinite power of the other.…
The near-unanimity-closed minions of Boolean functions, i.e., the clonoids whose target algebra contains a near-unanimity function, are completely described. The key concept towards this result is the minorant-minor partial order and its…
Let $V$ be a finite set of size $n$. We consider real functions on the "slice" $\binom{V}{k}$, which are also known as functions in the Johnson scheme. For $I \subseteq J \subseteq V$, the characteristic function of the set of all…
We first determine the maximal clones on a set X of infinite regular cardinality which contain all permutations but not all unary functions, extending a result of Heindorf's for countably infinite X. If |X| is countably infinite or weakly…