Large-scale distributed-memory machine designs represent a very attractive possibility for low-cost massively-parallel computation power. This work provides mathematical foundations of computing and computation theory by developing new models for designing, structuring, and analyzing software for such machines. The main objective of this research is to develop and refine modeling methodologies for parallel/distributed computations. These techniques will be based on the modeling and analysis capabilities of Extended Petri Nets and Communicating Finite Automata. In addition to the well- known properties of these modeling mechanisms, new properties of parallel computation behavior will be investigated, primarily influenced by relevant analytical properties from the field of control theory. This work forms a basis for new software development methodologies for parallel computers. Most significant will be its impact on improving the usability of the class of easy-to-build, but difficult-to-use, non- shared memory MIMD systems.
