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A109457 Number of Krom functions on n variables (or 2SAT instances): conjunctions of clauses with two literals per clause. +0
5
2, 4, 16, 166, 4170, 224716, 24445368, 5167757614, 2061662323954 (list; graph; listen)
OFFSET

0,1

COMMENT

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.

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

REFERENCES

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

D. E. Knuth, The Art of Computer Programming, Vol. 4, Section 7.1.1 (in preparation).

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.

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

CROSSREFS

Cf. A109458, A109459, A102897.

Cf. A112535.

Adjacent sequences: A109454 A109455 A109456 this_sequence A109458 A109459 A109460

Sequence in context: A073924 A061588 A050472 this_sequence A105788 A071008 A001146

KEYWORD

nonn,hard

AUTHOR

D. E. Knuth, Aug 24 2005

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Last modified October 13 20:18 EDT 2008. Contains 145016 sequences.


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