Semigroups and one-way functions

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3 Scopus citations


We study the complexity classes P and NP through a semigroup fP ("polynomial-time functions"), consisting of all polynomially balanced polynomial-time computable partial functions. The semigroup fP is non-regular if and only if P ≠ NP. The one-way functions considered here are based on worst-case complexity (they are not cryptographic); they are exactly the non-regular elements of fP. We prove various properties of fP, e.g. that it is finitely generated. We define reductions with respect to which certain universal one-way functions are fP-complete.

Original languageEnglish (US)
Pages (from-to)3-36
Number of pages34
JournalInternational Journal of Algebra and Computation
Issue number1-2
StatePublished - Apr 25 2015

All Science Journal Classification (ASJC) codes

  • Mathematics(all)


  • P vs. NP
  • Semigroups
  • regular semigroups

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