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A109457 Number of Krom functions on n variables (or 2SAT instances): conjunctions of clauses with two literals per clause. 5

%I #11 May 13 2018 10:17:57

%S 2,4,16,166,4170,224716,24445368,5167757614,2061662323954

%N Number of Krom functions on n variables (or 2SAT instances): conjunctions of clauses with two literals per clause.

%C A Krom function is equivalent to a Boolean function with the property that, if f(x)=f(y)=f(z)=1, then f(<xyz>)=1, where <xyz> denotes the bitwise median of the three Boolean vectors x, y, z.

%C Also related to number of retracts of an n-cube (see Feder).

%D Tomas Feder, Stable Networks and Product Graphs, Memoirs of the American Mathematical Society, 555 (1995), Section 3.2.

%D D. E. Knuth, The Art of Computer Programming, Vol. 4A, Section 7.1.1, p. 79.

%D Knuth, Donald E., Satisfiability, Fascicle 6, volume 4 of The Art of Computer Programming. Addison-Wesley, 2015, pages 148 and 220, Problem 191.

%D M. R. Krom, The decision problem for a class of first-order formulas in which all disjunctions are binary, Zeitschrift f. mathematische Logik und Grundlagen der Mathematik, 13 (1967), 15-20.

%D Thomas J. Schaefer, The complexity of satisfiability problems, ACM Symposium on Theory of Computing, 10 (1978), 216-226.

%Y Cf. A109458, A109459, A102897.

%Y Cf. A112535.

%K nonn,hard,more

%O 0,1

%A _Don Knuth_, Aug 24 2005

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