The distribution of Reversible Functions is Normal

Created by W.Langdon from gp-bibliography.bib Revision:1.4549

  author =       "W. B. Langdon",
  title =        "The distribution of Reversible Functions is {Normal}",
  booktitle =    "Genetic Programming Theory and Practice",
  publisher =    "Kluwer",
  year =         "2003",
  editor =       "Rick L. Riolo and Bill Worzel",
  chapter =      "11",
  pages =        "173--187",
  keywords =     "genetic algorithms, genetic programming, fitness
                 landscape, evolutionary computation, quantum computing,
                 CCNOT, Toffoli, low power consumption",
  ISBN =         "1-4020-7581-2",
  URL =          "",
  URL =          "",
  URL =          "",
  URL =          "",
  DOI =          "doi:10.1007/978-1-4419-8983-3_11",
  abstract =     "The distribution of reversible programs tends to a
                 limit as their size increases. For problems with a
                 Hamming distance fitness function the limiting
                 distribution is binomial with an exponentially small
                 chance (but non~zero) chance of perfect solution.
                 Sufficiently good reversible circuits are more common.
                 Expected RMS error is also calculated. Random unitary
                 matrices may suggest possible extension to quantum
                 computing. Using the genetic programming (GP)
                 benchmark, the six multiplexor, circuits of Toffoli
                 gates are shown to give a fitness landscape amenable to
                 evolutionary search. Minimal CCNOT solutions to the six
                 multiplexer are found but larger circuits are more
  notes =        "Extension of work presented at Dagstuhl See page 11 of
                 \cite{beyer_et_al:DSP:2006:498} Part of
  size =         "16 pages",

Genetic Programming entries for William B Langdon