For which sets A does there exist a mapping, computed by a total or partial recursive function, such that the mapping, when its domain is restricted to A, is a 1-to-1, onto mapping to Σ * ? And for which sets A does there exist such a mapping that respects the lexicographical ordering within A? Both cases are types of perfect, minimal hash functions. The complexity-theoretic versions of these n...

The current work introduces the notion of pdominant sets and studies their recursion-theoretic properties. Here a set A is called pdominant iff there is a partial A-recursive function ψ such that for every partial recursive function φ and almost every x in the domain of φ there is a y in the domain of ψ with y ≤ x and ψ(y) > φ(x). While there is a full Π 1 -class of nonrecursive sets where no s...

Recently, using a limit schema, we presented an analog and machine independent algebraic characterization of elementary functions over the real numbers in the sense of recursive analysis. In a different and orthogonal work, we proposed a minimalization schema that allows to provide a class of real recursive functions that corresponds to extensions of computable functions over the integers. Mixi...

Several important classes of normal logic programs includ ing the classes of acyclic acceptable and locally hierarchical programs have the property that every program in the class has a unique two valued supported model In this paper we call such classes unique sup ported model classes We analyse and characterize these classes by means of operators on three valued logics Our studies will motiva...

We study strictly level-decreasing logic programs (sld-programs) as defined earlier by the present authors. It will be seen that sld-programs, unlike most other classes of logic programs, have both a highly intuitive declarative semantics, given as a unique supported model, and are computationally adequate in the sense that every partial recursive function can be represented by some sld-program...

Using a C++ compiler, any partial recursive function can be computed at compile time. We show this by using the C++ template mechanism to define functions via primitive recursion, composition, and μ-recursion.