These lecture notes aim to provide a reasonably detailed introduction to some of the mathematics underpinning the theory of recursion and its interrelationships with proof theory. General results about hierarchies of “fast” and “slow” growing bounding functions are developed, in order: (i) to give a direct link between the computational complexity of recursions and the logical complexity of their termination proofs, and (ii) to show how the general notions of recursion and proof may be restricted so as to characterize computationally “realistic” complexity classes.
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