We define two extensions of the typed linear lambda-calculus that yield minimal Turingcomplete systems. The extensions are based on unbounded recursion in one case, and bounded recursion with minimisation in the other. We show that both approaches are compatible with linearity and typeability constraints. Both extensions of the typed linear lambda-calculus are minimal, in the sense that taking ...

This paper presents a simple and easy implementable Least Mean Square (LMS) type approach for frequency estimation of three phase power system in an unbalanced condition. The proposed LMS type algorithm is based on a second order recursion for the complex voltage derived from Clarke's transformation which is proved in the paper. The proposed algorithm is real adaptive filter with real parameter...

Primitive recursion is a well known syntactic restriction on recursive deenitions which guarantees termination. Unfortunately many natural deenitions, such as the most common deenition of Euclid's GCD algorithm, are not primitive recursive. Walther has recently given a proof system for verifying termination of a broader class of deenitions. Although Walther's system is highly automatible, the c...

In many cases, recursion removal improves the efficiency of recursive algorithms, especially algorithms with large formal parameters, such as All Pair Shortest path (APSP) algorithms. In this article, a recursion removal of the Seidel’s APSP [14] is presented, and a general method of recursion removal, called stack indexation is introduced.

We ask the attention for a de nition schema from higher order subrecursion the ory called bar recursion Bar recursion originates with Spector where bar recursion of all nite types is shown to characterize the class of provably total re cursive functions of analysis This class has also been characterized by Girard as those functions which are de nable in the second order typed lambda calculus or...