The importance of parallelism is difficult to overstate. As sequential computers have failed to meet modern computational challenges, engineers have begun to distribute computations across many processors, making prior algorithms immensely faster. Such a prevalent concept demands modelling so its power can be best understood. Many diverse models have been developed, ranging from pragmatic models like BSP and LogP, to theoretically involved and abstract ones like Parallel Turing Machines.
It is unfortunate then that a direct connection of results for classical Turing Machines to parallel complexity theory has seen little effort, with the only major model doing this being Parallel Turing Machines, proposed by Wiedermann. This model, while well-developed in its own right, only emulates shared memory parallelism, not accounting for message-passing distributed models like MapReduce. This makes it difficult to bring the hefty theory surrounding Turing Machines to bear on message-passing parallelism, with models like BSP and LogP giving little such theory and the LOCAL, ASYNC and CONGEST models focusing on communication challenges instead. Thus, it is harder to analyze problems such as how much faster an problem can be solved in a parallel message-passing environment than sequentially by a Turing Machine, a question that debatably defines the efficacy of such an approach to parallelism.
This project aims to produce a model that resolves this conundrum, linking Turing Machines and message-passing parallelism more strongly and providing an environment in which substantial complexity results can be produced. It should be noted that this project will restrict itself to classical computation, not straying into the domain of nonstandard models like quantum computing; these are beyond the scope of this project.