Narrow Results

A set $C$ of operations defined on a nonempty set $A$ is said to be a clone if $C$ is closed under composition of operations and contains all projection mappings. The concept of a clone belongs to the algebraic main concepts and has important applications in Computer Science. A clone can also be regarded as a many-sorted algebra where the sorts are the $n$-ary operations defined on set $A$ for all natural numbers $n\ge 1$ and the operations are the so-called superposition operations $S_m^n$ for natural numbers $m,n\ge 1$ and the projection operations as nullary operations. Clones generalize monoids of transformations defined on set $A$ and satisfy three clone axioms. The most important axiom is the superassociative law, a generalization of the associative law. If the superposition operations are partial, i.e. not everywhere defined, instead of the many-sorted clone algebra, one obtains partial many-sorted algebras, the partial clones. Linear terms, linear tree languages or linear formulas form partial clones. In this paper, we give a survey on partial clones and their properties.