Ackermann and the superpowers

@article{Porto1980AckermannAT,
  title={Ackermann and the superpowers},
  author={Ant{\'o}nio Porto and Armando B. Matos},
  journal={SIGACT News},
  year={1980},
  volume={12},
  pages={90-95}
}
The Ackermann function a(m, n) is a classical example of a total recursive function which is not primitive recursive. It grows faster than any primitive recursive function. It is usually defined by a general recurrence together with two “boundary” conditions. In this paper we obtain a closed form of a(m, n), which involves the Knuth superpower notation, namely a(m, n) = 2 m−2 ↑ (n + 3) − 3. Generalized Ackermann functions, that is functions satisfying only the general recurrence and one of the… 
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Primitive recursive functions versus partial recursive functions: comparing the degree of undecidability
TLDR
This work compares the degree of undecidability (measured by the level in the arithmetic hierarchy) of several primitive recursive decision problems with the corresponding problems of classical Recursion Theory.
Super-Exponentials Nonprimitive Recursive, but Rudimentary

References

SHOWING 1-2 OF 2 REFERENCES
Mathematics and Computer Science: Coping with Finiteness
TLDR
The distinction between finite and infinite is not as relevant as the distinction between realistic and unrealistic, and in many cases there are subtle ways to solve very large problems quickly, in spite of the fact that they appear at first to require examination of too many possibilities.
Decidability, Computability
  • 1969