Characterizations of closed classes of Boolean functions in terms of forbidden subfunctions and Post classes

Discrete Applied Mathematics

Volumn 149, Issue 1-3, 2005, Pages 200-218

  Zverovich, Igor E ^a  

^a RUTGERS UNIVERSITY   (United States)

Author keywords

Closed classes; Hereditary classes of Boolean functions; Post theorem

Indexed keywords

ALGEBRA; CHARACTERIZATION; GRAPH THEORY; THEOREM PROVING;

CLOSED CLASSES; HEREDITARY CLASSES OF BOOLEAN FUNCTIONS; POST THEOREM;

BOOLEAN FUNCTIONS;

EID: 22344444021     PISSN: 0166218X     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.dam.2004.06.028     Document Type: Article

References (36)

1. C. Benzaken Les familles de fonctions booleennes deduites de certaines familles de fonctions booleennes croissantes. Criteres de determination de l'indice d'une fonction croissante C. R. Acad. Sci. Paris 260 1965 1528 1531 (in French)
2. C. Benzaken Post's closed systems and the weak chromatic number of hypergraphs Discrete Math. 23 1978 77 84 (Reviewer D. de Werra)
3. C. Benzaken From logical gates synthesis to chromatic bicritical clutters Discrete Appl. Math. 96-97 1999 259 305
4. M. Davio, J.-P. Deschamps, A. Thayse, Discrete and switching functions, with a foreword by R. T. Yeh, (St-Saphorin), Georgi Publishing Company, Dusseldorf, McGraw-Hill, Switzerland, New York, 1978, xx+729 pp.
5. S. Foldes, G.R. Pogosyan, Post classes characterized by functional terms, RUTCOR Research Report RRR 32-2000, Rutgers University, 2000, 26pp.
6. G.P. Gavrilov Inductive representations of Boolean functions and the finite generation of the Post classes Algebra Logika 23 1 1984 3 26 (in Russian); translated in Algebra Logic 23 (1984) 1-19
7. G.P. Gavrilov, Functional Systems of Discrete Mathematics, Moscow State University, Moscow, 1985, 39 pp. (in Russian).
8. G.P. Gavrilov, A.A. Sapozhenko, Problems and Exercises in Discrete Mathematics, Kluwer Texts in the Mathematical Sciences, vol. 14, Kluwer Academic Publishers, Dordrecht, 1996, xi+422 pp.
9. S.G. Gindikin, Algebraic logic, Translated from the Russian by Robert H. Silverman, Problem Books in Mathematics, Springer, New York 1985, xviii+356 pp.
10. V.M. Glushkov, G.E. Tsejtlin, E.L. Yushchenko, Algebra. Languages. Programming Naukova Dumka, Kiev, 1974, 328 pp. (in Russian).
11. V.V. Gorlov On congruences in closed Post classes Math. Notes 13 1973 434 438
12. V.G. Karpov, V.A. Moshchenskii, Mathematical logic and discrete mathematics Vyshejsaya Shkola, Minsk, 1977, 254 pp. (in Russian).
13. A.D. Korshunov On the cardinality and structure of some closed Post classes (of families of subsets of a finite set) Dokl. Akad. Nauk SSSR 295 1987 533 537 (in Russian); translated in Sov. Math. Dokl. 36(1) (1988) 88-91
14. A.D. Korshunov, On the power and structure of closed Post classes (families of subsets of a finite set), Tr. Inst. Mat. (10) (1988) 159-204 (in Russian).
15. A.D. Korshunov, Families of subsets of a finite set and closed classes of Boolean functions, in: P. Frankl et al. (Eds.), Proceedings of the conference on extremal problems for finite sets, Visegrad, Hungary, 16-21 June, 1991, vol. 3, Bolyai Society for Mathematics Studies, Janos Bolyai Mathematical Society, Budapest, 1994, pp. 375-396.
16. J. Kuntzmann, Algebre de Boole, Dunod, Paris, 1965, xxii + 319 pp. (in French).
17. S.S. Marchenkov Existence of finite bases in closed classes of Boolean functions Algebra Logika 23 1 1984 88 99 (in Russian); translated in Algebra Logic 23 (1984) 66-74
18. S.S. Marchenkov The invariants of Post classes Fundam. Prikl. Mat. 4 4 1998 1385 1404 (in Russian)
19. S.S. Marchenkov, Closed Classes of Boolean Functions, Nauka, Fizmatlit, Moscow, 2000, 126 pp. (in Russian).
20. S.S. Marchenkov, Closed Classes of Boolean Functions, second ed., Fizmatlit, Moscow, 2001, 128 pp. (in Russian).
21. S.S. Marchenkov, A.B. Ugol'nikov, Closed classes of Boolean functions, Institut Prikladnoj Matematiki Im. M. V. Keldysha, Moscow, 1990, 148 pp. (in Russian).
22. A. Mukhopadhyay Complete sets of logic primitives Recent Developments in Switching Theory 1971 Academic Press New York 1 26
23. F.J. Pelletier, and N.M. Martin Post's functional completeness theorem Notre Dame J. Formal Logic 31 3 1990 462 475
24. N. Pippenger, Theories of Computability, Cambridge University Press, Cambridge, 1997, ix+251 pp.
25. E. Post Introduction to a general theory of elementary propositions Amer. J. Math. 43 1921 163 185
26. E. Post, Two-Valued Iterative Systems of Mathematical Logic, Annals of Mathematical Studies, vol. 5, Princeton University Press, Princeton, NJ, 1941.
27. M. Reschke, and K. Denecke A new proof of E. L. Post's results on closed classes of Boolean functions J. Inform. Process. Cybernet. 25 7 1989 361 380 (in German)
28. M. Reschke, O. Lüders, and K. Denecke Congruence distributivity, congruence permutability and congruence modularity of two-element algebras J. Inform. Process. Cybernet. 24 1-2 1988 65 78 (in German)
29. I. Rosenberg Compositions of functions on finite sets D.C. Rine Computer Science and Multiple-valued Logic. Theory and Applications 1977 North-Holland Amsterdam, New York, Oxford
30. G.A. Shestopal Simple bases in closed classes of functions of the algebra of logic Dokl. Akad. Nauk SSSR 168 1966 1023 1026 (in Russian); translated in Sov. Math. Dokl. 7 (1966) 792-795
31. G.A. Shestopal Simple bases in all closed classes of functions of the algebra of logic Uch. Zapiski MGPI im. V. I. Lenina 375 1971 156 178
32. V.A. Stetsenko, On a classification of Post classes, Veroyatn. Metody Kibern. (23) (1987) 110-119 (in Russian).
33. A.B. Ugol'nikov On closed Post classes Izv. Vyssh. Uchebn. Zaved., Mat. 7 314 1988 79 88 (in Russian); translated in Sov. Math. 32(7) (1988) 131-142
34. 2, Problemy Kibernetiki, vol. 39, Nauka, Moscow, 1982, pp. 262.
35. S.V. Yablonsky, Introduction to Discrete Mathematics, second ed., Nauka, Moscow, 1986, 384 pp. (in Russian).
36. S.V. Yablonsky, G.P. Gavrilov, V.B. Kudrjavtsev, Functions Algebra of Logics and Post Classes, Nauka Glavnaya Redaktsiya Fiz.-Mat. Lit., Moscow, 1966, 115 pp. (in Russian).