This site is supported by donations to The OEIS Foundation.

 Annual Appeal: Please make a donation to keep the OEIS running. In 2018 we replaced the server with a faster one, added 20000 new sequences, and reached 7000 citations (often saying "discovered thanks to the OEIS"). Other ways to donate

 Hints (Greetings from The On-Line Encyclopedia of Integer Sequences!)
 A056287 Maximal AND-OR formula complexity (operator count) for n-input Boolean functions 4
 1, 3, 9, 15, 28 (list; graph; refs; listen; history; text; internal format)
 OFFSET 1,2 COMMENTS a(n) = minimal number of edges in 2-terminal series-parallel switching network (where edges are labeled with the variables X_i and X_i') which achieves the worst f. Consider all 2^2^n Boolean functions f of n variables X_1, ..., X_n; the X_i's and their negated values X_1', ..., X_n' are available and we must realize f using AND's and OR's of these 2n variables with the smallest total number of AND's and OR's; call the minimal total number of AND's and OR's used G(f); then a(n) = max G(f). LINKS Russ Cox, Notes on computing a(4) Russ Cox, Minimum Boolean Formulas EXAMPLE For n=2 a worst f is X XOR Y, which can be realized by X AND Y' OR X' AND Y = XY' + X'Y. For n=3 a worst f is X XOR Y XOR Z, which can be realized by (X*Z'+X'*Z+Y')*(X*Z+X'*Z'+Y). For n=4 a worst f is W XOR X XOR Y XOR Z, which can be realized by ((X XOR Z)'+(W XOR Y)')*((X XOR Z)+(W XOR Y)) = (X*Z'+X'*Z+W'*Y+W*Y')*(X*Z+X'*Z'+W*Y+W'*Y'). For n=5 there are three worst f's up to permutation and negation of input variables. They have 32-bit truth tables 0x16686997, 0x16696997 and 0x1669e996 (in hexadecimal). CROSSREFS Cf. A058759, A057241, A178939. Sequence in context: A131801 A280963 A122819 * A099409 A002127 A061810 Adjacent sequences:  A056284 A056285 A056286 * A056288 A056289 A056290 KEYWORD nonn,nice,hard,more AUTHOR N. J. A. Sloane, Jan 05 2001 EXTENSIONS a(3) and a(4) computed by Russ Cox, Jan 03 2001 a(5) computed by Russ Cox and Alex Healy, Jul 12 2010 STATUS approved

Lookup | Welcome | Wiki | Register | Music | Plot 2 | Demos | Index | Browse | More | WebCam
Contribute new seq. or comment | Format | Style Sheet | Transforms | Superseeker | Recent
The OEIS Community | Maintained by The OEIS Foundation Inc.

Last modified December 19 03:45 EST 2018. Contains 318245 sequences. (Running on oeis4.)