Distributed Computation as Hierarchy

This paper presents a new distributed computational model of distributed systems called the phase web that extends Vaughn Pratt’s orthocurrence relation from 1986. The model uses mutual-exclusion to express sequence, and a new kind of hierarchy to replace event sequences, posets, and pomsets. The model explicitly connects computation to a discrete Clifford algebra that is in turn extended into homology and co-homology, wherein the recursive nature of objects and boundaries becomes apparent and itself subject to hierarchical recursion. Topsy, a programming environment embodying the phase web, is currently being readied for release.