Exploring the Equivalence between Dynamic Dataflow Model and Gamma - General Abstract Model for Multiset mAnipulation

Rui R. Mello Junior, Leandro S. Araujo, Tiago A. O. Alves, Leandro A. J. Marzulo, Gabriel A. L. Paillard, Felipe M. G. França

With the increase of the search for computational models where the expression of parallelism occurs naturally, some paradigms arise as options for the next generation of computers. In this context, dynamic Dataflow and Gamma - General Abstract Model for Multiset mAnipulation) - emerge as interesting computational models choices. In the dynamic Dataflow model, operations are performed as soon as their associated operators are available, without rely on a Program Counter to dictate the execution order of instructions. The Gamma paradigm is based on a parallel multiset rewriting scheme. It provides a non-deterministic execution model inspired by an abstract chemical machine metaphor, where operations are formulated as reactions that occur freely among matching elements belonging to the multiset. In this work, equivalence relations between the dynamic Dataflow and Gamma paradigms are exposed and explored, while methods to convert from Dataflow to Gamma paradigm and vice versa are provided. It is shown that vertices and edges of a dynamic Dataflow graph can correspond, respectively, to reactions and multiset elements in the Gamma paradigm. Implementation aspects of execution environments that could be mutually beneficial to both models are also discussed. This work provides the scientific community with the possibility of taking profit of both parallel programming models, contributing with a versatility component to researchers and developers. Finally, it is important to state that, to the best of our knowledge, the similarity relations between both dynamic Dataflow and Gamma models presented here have not been reported in any previous work.

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