We know about calculability of a function or computability. We looks for the ability to solve a specific problem / compute a function with calculus method.

But if we define a calculus method, is there a way to find generals limits of the method ?

Can we say that if the method can give same results as logical connective/operators, this method would solved anything computable by logical operators ?


I an other way the question could be : How can we define the "computation power" or "computability space" of a method (Turing machine, logical operators, lambda cacul, celular automaton, etc....) ?

  • $\begingroup$ Your question is not clear. Can you change it to give examples of what you mean? $\endgroup$ – Andrej Bauer May 22 '18 at 8:25
  • $\begingroup$ @AndrejBauer edited my post, is it better ? $\endgroup$ – Dadep May 22 '18 at 8:32
  • $\begingroup$ Yes, I think it's better, but you can also change the original question and the title. For instance, when you say "calculus method", do you mean "calculus as in mathematical analysis (derivatives, integrals)" or do you mean "calculus" in the general sense? The title is already possibly misleading, if you know how to fix it, that would be helpful. $\endgroup$ – Andrej Bauer May 22 '18 at 9:00
  • $\begingroup$ @AndrejBauer, I mean calculus in general sense, If you have any suggestion to change title it is very welcome ! $\endgroup$ – Dadep May 22 '18 at 9:06
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    $\begingroup$ I think you might be wondering how, given a definition of some computation model (e.g. a given programming language, or a class of automata possibly affecting stacks/queues/tapes/grids), we can assess its computational power, for instance comparing it against PDAs, TMs, or the like. What you call "calculus" is probably meant to be "computation". In general, there is no fast universal method to solve that: often, one tries to simulate one model inside another one to prove that the latter is at least as powerful. $\endgroup$ – chi May 22 '18 at 11:44

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