Title:  Modeling Discrete Slowdown

Abstract: Discrete systems often process infinite streams of input values, using these to produce infinite streams of output values.  Streams input to a program can slow down; in this paper we consider those streams which slow down by repeating their values. We provide two retiming concepts called discrete time transforms and latency functions which can be used to express the relationship between a trace and a slower version of that trace. These two concepts are then shown to be equally expressive. When an input stream to a discrete system slows down in the manner described, the system will react in a certain way. However, not all systems react in desirable ways. We conclude by giving a number of well behaviour properties which systems may satisfy, which guarantee a certain pattern of behaviour under discrete slowdown.