Mathematical Foundation of the Synchronous/Reactive Model

The Synchronous/Reactive Model is built upon three mathematical concepts: Theorem 2 on page 48 of [1] 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.

The Synchronous/Reactive model of computation requires that the blocks (actors) be monotonic functions. Pages 50-52 of [1] 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

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to mean the least upper bound. He also uses poset as an abbreviation for a partially-ordered set.


  1. 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.

Updated 04/22/02.