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Mechanisation of the AKS Algorithm

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Abstract

The AKS algorithm (by Agrawal, Kayal and Saxena) is a significant theoretical result, establishing “PRIMES in P” by a brilliant application of ideas from finite fields. This paper describes an implementation of the AKS algorithm in our theorem prover HOL4, together with a proof of its correctness and its computational complexity. The complexity analysis is based on a conservative computation model using a writer monad. The method is elementary, but enough to show that our implementation of the AKS algorithm takes a number of execution steps bounded by a polynomial function of the input size. This establishes formally that the AKS algorithm indeed shows “PRIMES is in P”.

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Authors and Affiliations

  1. Australian National University, Canberra, Australia

    Hing Lun Chan & Michael Norrish

  2. Canberra Research Laboratory, Data61, Canberra, Australia

    Michael Norrish

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  1. Hing Lun Chan
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Correspondence to Hing Lun Chan.

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Chan, H.L., Norrish, M. Mechanisation of the AKS Algorithm. J Autom Reasoning 65, 205–256 (2021). https://doi.org/10.1007/s10817-020-09563-y

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