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2010 | 30 | 1 | 7-33
Tytuł artykułu

The submaximal clones on the three-element set with finitely many relative R-classes

Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
For each clone C on a set A there is an associated equivalence relation analogous to Green's R-relation, which relates two operations on A if and only if each one is a substitution instance of the other using operations from C. We study the maximal and submaximal clones on a three-element set and determine which of them have only finitely many relative R-classes.
Słowa kluczowe
Rocznik
Tom
30
Numer
1
Strony
7-33
Opis fizyczny
Daty
wydano
2010
otrzymano
2009-05-01
poprawiono
2009-07-30
Twórcy
  • University of Luxembourg 6, rue Richard Coudenhove-Kalergi L-1359 Luxembourg, Luxembourg
  • Department of Mathematics University of Colorado at Boulder Campus Box 395 Boulder, CO 80309-0395, USA
  • Bolyai Institute Aradi vértanúk tere 1, H-6720 Szeged, Hungary
Bibliografia
  • [1] G.A. Burle, The classes of k-valued logics containing all one-variable functions, Diskretnyi Analiz 10 (1967), 3-7.
  • [2] J. Demetrovics and J. Bagyinszki, The lattice of linear classes in prime-valued logics, in: J.L. Kulikowski, M. Michalewicz, S.V. Yablonskii, Yu.I. Zhuravlev (eds.), Discrete Mathematics (Warsaw, 1977), Banach Center Publ. 7, PWN, Warsaw (1982), pp. 105-123.
  • [3] A. Feigelson and L. Hellerstein, The forbidden projections of unate functions, Discrete Appl. Math. 77 (1997), 221-236. doi: 10.1016/S0166-218X(96)00136-9
  • [4] M.A. Harrison, On the classification of Boolean functions by the general linear and affine groups, J. Soc. Indust. Appl. Math. 12 (2) (1964), 285-299. doi: 10.1137/0112026
  • [5] J. Henno, Green's equivalences in Menger systems, Tartu Riikl. Ül. Toimetised 277 (1971), 37-46.
  • [6] D. Lau, Submaximale Klassen von P₃, Elektron. Informationsverarb. Kybernet. 18 (1982), 227-243.
  • [7] D. Lau, Function Algebras on Finite Sets, Springer-Verlag, Berlin, Heidelberg 2006.
  • [8] E. Lehtonen, Descending chains and antichains of the unary, linear, and monotone subfunction relations, Order 23 (2006), 129-142. doi: 10.1007/s11083-006-9036-y
  • [9] E. Lehtonen and Á. Szendrei, Equivalence of operations with respect to discriminator clones, Discrete Math. 309 (2009), 673-685. doi: 10.1016/j.disc.2008.01.003
  • [10] E. Lehtonen and Á. Szendrei, Clones with finitely many relative R-classes, arXiv:0905.1611.
  • [11] H. Machida, On closed sets of three-value monotone logical functions, in: B. Csákány, I. Rosenberg (eds.), Finite Algebra and Multiple-Valued Logic (Szeged, 1979), Colloq. Math. Soc. János Bolyai 28, North-Holland, Amsterdam (1981), pp. 441-467.
  • [12] S.S. Marchenkov, J. Demetrovics and L. Hannák, Closed classes of self-dual functions in P₃, Metody Diskret. Anal. 34 (1980), 38-73.
  • [13] N. Pippenger, Galois theory for minors of finite functions, Discrete Math. 254 (2002), 405-419. doi: 10.1016/S0012-365X(01)00297-7
  • [14] R. Pöschel and L.A. Kalužnin, Funktionen- und Relationenalgebren: Ein Kapitel der diskreten Mathematik, Birkhäuser, Basel, Stuttgart 1979.
  • [15] I.G. Rosenberg, Über die funktionale Vollständigkeit in den mehrwertigen Logiken, Rozpravy Československé Akad. Věd, Řada Mat. Přírod. Věd 80 (1970), 3-93.
  • [16] J. Słupecki, Kryterium pełności wielowartościowych systemów logiki zdań, C.R. Séanc. Soc. Sci. Varsovie, Cl. III 32 (1939), 102-109. English translation: A criterion of fullness of many-valued systems of propositional logic, Studia Logica 30 (1972), 153-157. doi: 10.1007/BF02120845
  • [17] Á. Szendrei, Clones in Universal Algebra, Séminaire de mathématiques supérieures 99, Les Presses de l'Université de Montréal, Montréal 1986.
  • [18] C. Wang, Boolean minors, Discrete Math. 141 (1995), 237-258. doi: 10.1016/0012-365X(93)E0191-6
  • [19] C. Wang and A.C. Williams, The threshold order of a Boolean function, Discrete Appl. Math. 31 (1991), 51-69. doi: 10.1016/0166-218X(91)90032-R
  • [20] S.V. Yablonsky, Functional constructions in a k-valued logic, Trudy Mat. Inst. Steklov. 51 (1958), 5-142.
  • [21] I.E. Zverovich, Characterizations of closed classes of Boolean functions in terms of forbidden subfunctions and Post classes, Discrete Appl. Math. 149 (2005), 200-218. doi: 10.1016/j.dam.2004.06.028
Typ dokumentu
Bibliografia
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bwmeta1.element.bwnjournal-article-doi-10_7151_dmgaa_1160
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