DOI QR코드

DOI QR Code

Variants of Essential Arity for Partial Functions

  • Received : 2018.11.07
  • Accepted : 2019.08.22
  • Published : 2020.09.30

Abstract

Generalizations of essential arity of partial functions, based on essential sets of arguments, are introduced, and their interplay with the minor relation of functions is investigated.

Keywords

References

  1. J. Berman and A. Kisielewicz, On the number of operations in a clone, Proc. Amer. Math. Soc., 122(1994), 359-369. https://doi.org/10.1090/S0002-9939-1994-1198450-9
  2. Y. Breitbart, Essential variables of functions of the algebra of logic, in Russian, Dokl. Akad. Nauk USSR, 172(1967), 9-10.
  3. K. N. Cimev, Separable sets of arguments of functions, Studies 180/1986, Computer and Automation Institute, Hungarian Academy of Sciences, Budapest, 1986.
  4. M. Couceiro and S. Foldes, On closed sets of relational constraints and classes of functions closed under variable substitutions, Algebra Universalis, 54(2005), 149-165. https://doi.org/10.1007/s00012-005-1933-1
  5. M. Couceiro and E. Lehtonen, On the effect of variable identification on the essential arity of functions on finite sets, Internat. J. Found. Comput. Sci., 18(2007), 975-986. https://doi.org/10.1142/S012905410700508X
  6. M. Couceiro and E. Lehtonen, Generalizations of Swierczkowski's lemma and the arity gap of finite functions, Discrete Math., 309(2009), 5905-5912. https://doi.org/10.1016/j.disc.2009.04.009
  7. M. Couceiro and E. Lehtonen, On the arity gap of finite functions: results and applications, J. Mult.-Valued Logic Soft Comput., 27(2016), 193-207.
  8. R. O. Davies, Two theorems on essential variables, J. London Math. Soc., 41(1966), 333-335. https://doi.org/10.1112/jlms/s1-41.1.333
  9. K. Denecke and J. Koppitz, Essential variables in hypersubstitutions, Algebra Universalis, 46(2001), 443-454. https://doi.org/10.1007/PL00000353
  10. A. Ehrenfeucht, J. Kahn, R. Maddux and J. Mycielski, On the dependence of functions on their variables, J. Combin. Theory Ser. A, 33(1982), 106-108. https://doi.org/10.1016/0097-3165(82)90084-X
  11. O. Ekin, S. Foldes, P. L. Hammer and L. Hellerstein, Equational characterizations of Boolean function classes, Discrete Math., 211(2000), 27-51. https://doi.org/10.1016/S0012-365X(99)00132-6
  12. E. Lehtonen, Reconstruction of functions from minors, Habilitation thesis, Technische Universitat Dresden, Dresden, 2018. http://nbn-resolving.de/urn:nbn:de:bsz:14-qucosa-237864
  13. N. Pippenger, Galois theory for minors of finite functions, Discrete Math., 254(2002), 405-419. https://doi.org/10.1016/S0012-365X(01)00297-7
  14. A. Salomaa, On essential variables of functions, especially in the algebra of logic, Ann. Acad. Sci. Fenn. Ser. A I. Math., 339(1963), 11 pp.
  15. B. S. W. Schroder, Ordered sets: An introduction, Birkhauser, Basel, 2003.
  16. S. Shtrakov, Essential arity gap of Boolean functions, Serdica J. Comput., 2(2008), 249-266.
  17. R. Willard, Essential arities of term operations in finite algebras, Discrete Math., 149(1996), 239-259. https://doi.org/10.1016/0012-365X(94)00323-B
  18. R. O. Winder, Fundamentals of threshold logic, Applied Automata Theory, 235-318, Academic Press, New York, 1968.