@article{paolini2020tcs,
  volume = {813},
  author = {Luca Paolini and Mauro Piccolo and Luca Roversi},
  issn = {0304-3975},
  keywords = {Reversible computation, Unconventional computing models,
              Computable permutations, Primitive recursive functions, Recursion
              theory},
  url = {http://www.sciencedirect.com/science/article/pii/S0304397519307558},
  abstract = {We focus on total functions in the theory of reversible
              computational models. We define a class of recursive permutations,
              dubbed Reversible Primitive Permutations (RPP) which are
              computable invertible total endo-functions on integers, so a
              subset of total reversible computations. RPP is generated from
              five basic functions (identity, sign-change, successor,
              predecessor, swap), two notions of composition (sequential and
              parallel), one functional iteration and one functional selection.
              RPP is closed by inversion and it is expressive enough to encode
              Cantor pairing and the whole class of Primitive Recursive
              Functions.},
  title = {A class of Recursive Permutations which is Primitive Recursive
           complete},
  pages = {218 - 233},
  journal = {Theoretical Computer Science},
  doi = {https://doi.org/10.1016/j.tcs.2019.11.029},
  year = {2020},
}

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