A labelled transition system is provided with some additional structure by endowing the conngurations and the labels with a complete metric. In this way, a so-called metric labelled transition system is obtained. The additional structure on a metric labelled transition system makes it possible to generalize the niteness conditions nitely branching and image nite to compactly branching and image...

I present a criterion for all-order finiteness in N =1 SYM theories. Three applications are given; they yield all-order finite N=1 SYM models with global symmetries of the superpotential. 1. INTRODUCTION The aim of this paper is to present applications of the criterion for all-order finiteness in N = 1 SYM of [ 1]. All-order finiteness is here meant in the sense of exact vanishing of the pertur...