Recursion-closed algebraic theories

Recursion-Closed Algebraic Theories

A class of algebraic theories called “recursion-closed,” which generalize the rational theories studied by J. A. Goguen, J. W. Thatcher, E.G. Wagner and J. B. Wright in [in “Proceedings, 17th IEEE Symposium on Foundations of Computer Science, Houston, Texas, October 1976,” pp. 147-158; in “Mathematical Foundations of Computer Science, 1978,” Lecture Notes in Computer Science, Vol. 64, Springer-...

An Algebraic Treatment of Recursion

Jan Bergstra has put his mark on theoretical computer science by a consistent stream of original ideas, controversial opinions, and novel approaches. He sometimes reorganised the arena, enabling others to follow. I, for one, might never have entered computer science if it wasn’t for Jan’s support and encouragement, and will never forget the team spirit in the early days of process algebra in hi...

Algebraic theories

We presents the algebraic theories over an arbitrary monoid, main properties and calculus rules. Ordered, rationaly closed and ω-continuous theories on one hand and matrix and complete matrix theories on the other hand are the presentation main subjects. Some examples comming from algebra and computer science finish this paper.

Reducing Recursion to Iteration by Algebraic Extension

Simple recursion relations for general field theories

On-shell methods offer an alternative definition of quantum field theory at treelevel, replacing Feynman diagrams with recursion relations and interaction vertices with a handful of seed scattering amplitudes. In this paper we determine the simplest recursion relations needed to construct a general four-dimensional quantum field theory of massless particles. For this purpose we define a coverin...