Mathematical Foundation of the Synchronous/Reactive Model
The Synchronous/Reactive Model is built upon three mathematical
Theorem 2 on page 48 of  proves that "an SR system always has
a unique behavior, and its proof contains the fundamental idea
used to evaluate the systems".
The proof relies on Proposition 6 which states that a continuous
function is monotonic.
- complete partial order (CPO): "a set with an abstract notion of
the amount of 'information' in each element." 
see Definitions 1-4 in chapter 3 of 
- monotonic function: "applying a monotonic function to an element
of CPO always increases the amount of information, unless it is
a fixed point, in which case the element is unchanged." 
see Definition 6 in chapter 3 of 
- fixed point: given the vector x in which each element of x
belongs to a CPO, then x is a fixed point for a function f
if f(x) = x.
see Definition 8 in chapter 3 of 
The Synchronous/Reactive model of computation requires that the
blocks (actors) be monotonic functions.
Pages 50-52 of  show that the Synchronous/Reactive model is
deterministic because an SR graph always has a least fixed point.
Note that in Stephen's thesis, he uses the symbol
to mean the least upper bound.
He also uses poset as an abbreviation for a partially-ordered set.
- Stephen Anthony Edwards, The Specification and Execution
of Synchronous Reactive Systems,
Ph.D. Thesis, University of California, Berkeley, 1997,
Available as UCB/ERL M97/31.