Using Set Rewriting to Implement the Chemical Reaction Computation Model

Abstract

The Gamma formalism and its chemical computation model is a good theoretical formalism for parallel computations. But the lack of implementations that can be used in practice has reduced its impact. This paper introduces a new and original implementation of the Gamma formalism based on set rewriting, that has the potential of reviving it from a practical point of view. The multisets are the basic data structure used by the Gamma formalism, so the quality of any implementation for this formalism depends on the quality of the implementation of the multiset. Set rewriting enables term rewriting on all the terms of a given set in a single rewriting operation, thus executing several rewriting operations in parallel and at the cost of a single one. The use of set rewriting to implement the multiset and the actions of the Gamma formalism seems to be a natural match, as they are both based on non -deterministic, parallel processing. The paper describes the new implementation and presents a proof of concept for the Gamma program for sorting numbers.