Polynomial-time right-ideal morphisms and congruences

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We continue with the functional approach to the P-versus-NP problem, begun in [J. C. Birget, Semigroups and one-way functions, Int. J. Algebra Comput. 25(1-2) (2015) 3-36; J. C. Birget, Infinitely generated semigroups and polynomial complexity, Int. J. Algebra Comput. 26(04) (2016) 727-750.] We previously constructed a monoid P that is non-regular iff NP P. We now construct homomorphic images of P with interesting properties. In particular, the homomorphic image polyP of P is finitely generated, and is non-regular iff P NP. The group of units of polyP is the famous Richard Thompson group V.

Original languageEnglish (US)
Pages (from-to)791-835
Number of pages45
JournalInternational Journal of Algebra and Computation
Issue number5
StatePublished - Aug 1 2018

All Science Journal Classification (ASJC) codes

  • Mathematics(all)


  • P -versus- NP
  • Semigroups
  • regular semigroups

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