A Topological Model for Parallel Algorithm Design
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This research demonstrates that formal, mathematical analysis in theoretical computer science can be recast in terms of the topology of complete metric spaces, and also presents a methodical technique for developing formal specifications. This effort shows that the topology of complete metric spaces provides a tool that can be used to both recreate major results about computational models and also to develop new results about these models. Using the two computational models CSP and UNITY, this effort shows that the required mathematics needed to support this alternative to the traditional analysis of computational models can be readily supported by a standard course sequence in real analysis. Since the approach of proving programs correct after being written has not been widely accepted, this effort presents an alternative approach based on the developed topological framework for the formal specification language UNITY. this approach, designed to be automated, uses a set of transformations applied to UNITY specifications that preserve desired program properties.
- Theoretical Mathematics
- Computer Programming and Software