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Does anyone know of an accessible introduction to Cobham's model independent characterization of FP and it's equivalence to the standard definition using Turing machines? The best source I could find on-line was https://www.cs.toronto.edu/~sacook/homepage/ptime.pdf : a paper by Stephen Bellantoni and Stephen Cook detailing another similar approach. However, it is a little too difficult for me to understand.

As a side question, does anyone know if researchers are still interested in Cobham's formulation or feel it could possibly lead to resolving open problems?

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  • $\begingroup$ I'm not sure how accessible you expect a recursion-theoretic characterization of polynomial time to be. Such things are necessarily very technical and they're difficult to understand because they involve difficult concepts. $\endgroup$ – David Richerby Jun 25 '15 at 20:57
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    $\begingroup$ @DavidRicherby I'm mainly interested in just the basic functions it entails because I know at least that FP is the class closed under certain operations and functions (one I think is called the "smash" function, but I don't know its formal definition). I guess the equivalence proof will be beyond my reach at this point. $\endgroup$ – Ari Jun 25 '15 at 21:07

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