Are there other computer architectures apart from the Von Neumann /Turing architecture?
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Turing machine is an abstract computational model which has its strengths and weaknesses. Von Neumann architecture is a way to implement it. There are several other computational models. You can find a list of many of them here
Single-instruction, multiple data (SIMD) and Multiple-instruction, multiple-data MIMD architectures have one or more streams of instructions operating on more than one stream of data. These architectures have been realised by machines such as the old Crays, Vector processors, and Connection Machines, which differ significantly from Von Neumann machines as they break away from the single instruction sequence and a single data stream model. More exotic architectures have been proposed, inspired by biology such as the cellular architecture and systolic arrays, named after analogy with the regular pumping of blood by the heart.
The less general purpose these architectures are the more difficult they are to program, except for a special class of problems; for problems in this class, highly efficient implementations are possible, as the "abstractions" of the problem match the topology and other features of the architecture.