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    This study was inspired by recent successful applications of evolutionary computation to the problem of finding terms to represent arbitrarily given operations on a primal groupoid. Evolution requires that small changes in a term result in small changes in the associated term operation. We prove a theorem giving two readily testable conditions under which a groupoid must have this continuity property, and offer evidence that most primal groupoids satisfy these conditions.

    AMSC: 08A40, 68Q05, 92D15


    • D. Clarket al., Algebra Universalis 63(4), 303 (2010). Crossref, ISIGoogle Scholar
    • D. Clark, M. Keijzer and L. Spector, Evolution of algebraic terms 2: Algorithms and applications, preprint . Google Scholar
    • A. E.   Eiben and J. E.   Smith , Introduction to Evolutionary Computing ( Springer-Verlag , 2008 ) . Google Scholar
    • R. Freese, UACalc, a Universal algebra calculator (2008), . Google Scholar
    • V. L.   Murskıĭ , Problémy Kibérnétiki   30 , 43 ( 1975 ) . Google Scholar
    • R. W. Quackenbush, Finite Algebra and Multiple-Valued Logic, Colloquia Mathematica Societatis János Bolyai 28 (North-Holland, 1981) pp. 603–634. Google Scholar
    • I.   Rosenberg , Rozpravy Československé Akad. Věd Řada Mat. Pří rod.   80 , 1 ( 1970 ) . Google Scholar
    • G.   Rousseau , Proc. Amer. Math. Soc.   18 , 1009 ( 1967 ) . Crossref, ISIGoogle Scholar
    • H. M.   Sheffer , Trans. Amer. Math. Soc.   14 , 481 ( 1913 ) . CrossrefGoogle Scholar
    • L. Spectoret al., Genetic programming for finite algebras, Genetic and Evolutionary Computation Conference (GECCO) 2008 Proc, ed. M. Keijzer (Association for Computing Machinery, 2008) pp. 1291–1298. Google Scholar
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