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As others have pointed out, "model of computation" is an open-ended concept that can hardly be captured by a single defintion. A similar example in traditional mathematics is "space". However, this should not prevent us from giving precise definitions of "model of computation". As our understanding and motivations change, so will the definitions. And keep ...


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I think that different mathematical models of computation capture different aspects of physical reality. Similar to models of solid state physics (say), these mathematical models may be largely incomparable. Think of analog computers, where the model may not even be described with discrete math. When it comes to automata and formal languages (of finite words ...


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https://www.staff.science.uu.nl/~ooste110/talks/NMC53.pdf this reference says MoC’s are structured in a category (in fact, a 2-category).


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