Re: Simplify needs ages to finish

*To*: mathgroup at smc.vnet.net*Subject*: [mg44792] Re: Simplify needs ages to finish*From*: Don Taylor <dont at agora.rdrop.com>*Date*: Thu, 27 Nov 2003 11:38:16 -0500 (EST)*Sender*: owner-wri-mathgroup at wolfram.com

Sorry to trouble you but Newsgroups.com appears to have broken moderation again, We got them to fix this once and I have no idea what they did now. Would you be so kind and post this as a follow-up to the recent posting with this subject line? It was posted a few days ago. Thank you In comp.soft-sys.math.mathematica you write: >I've got the following simple (well, IMO) boolean equations and can't >believe that it takes more than 2 hours on an Intel(R) Xeon(TM) CPU >2.00GHz to evaluate the last output: foo[a1, a2, a3, a4, b1, b2, b3, b4] >I'm using mathematica 4.1. .. >foo[a1_, a2_, a3_, a4_, b1_, b2_, b3_, b4_] := > Simplify[Xor[oparity[a1, a2, a3, a4, b1, b2, b3, b4], > !oparity[!a1, !a2, !a3, !a4, !b1, !b2, !b3, !b4]]]; >foo[a1, a2, a3, a4, b1, b2, b3, b4] I fiddled with this for a while. Finally I wrote some really awful code and created an 8-variable k-map for foo[]. This evaluates in seconds. I hope I haven't made a mistake in this. This needs just the right fixed width font and squint your eyes really tight to see the pretty pattern that is hiding inside his data, substituting True->1 and False->0. {{1,0,1,1,1,0,0,1,1,0,1,1,1,1,0,1}, {0,1,1,1,0,1,1,0,0,1,1,1,1,1,1,0}, {1,1,1,0,0,1,1,0,1,1,1,0,0,1,1,1}, {1,1,0,1,1,0,0,1,1,1,0,1,1,0,1,1}, {1,0,0,1,1,0,1,1,1,1,0,1,1,0,1,1}, {0,1,1,0,0,1,1,1,1,1,1,0,0,1,1,1}, {0,1,1,0,1,1,1,0,0,1,1,1,1,1,1,0}, {1,0,0,1,1,1,0,1,1,0,1,1,1,1,0,1}, {1,0,1,1,1,1,0,1,1,0,1,1,1,0,0,1}, {0,1,1,1,1,1,1,0,0,1,1,1,0,1,1,0}, {1,1,1,0,0,1,1,1,1,1,1,0,0,1,1,0}, {1,1,0,1,1,0,1,1,1,1,0,1,1,0,0,1}, {1,1,0,1,1,0,1,1,1,0,0,1,1,0,1,1}, {1,1,1,0,0,1,1,1,0,1,1,0,0,1,1,1}, {0,1,1,1,1,1,1,0,0,1,1,0,1,1,1,0}, {1,0,1,1,1,1,0,1,1,0,0,1,1,1,0,1}} Even easier to see, comma->space and True->. and False->0. {{. 0 . . . 0 0 . . 0 . . . . 0 .} {0 . . . 0 . . 0 0 . . . . . . 0} {. . . 0 0 . . 0 . . . 0 0 . . .} {. . 0 . . 0 0 . . . 0 . . 0 . .} {. 0 0 . . 0 . . . . 0 . . 0 . .} {0 . . 0 0 . . . . . . 0 0 . . .} {0 . . 0 . . . 0 0 . . . . . . 0} {. 0 0 . . . 0 . . 0 . . . . 0 .} {. 0 . . . . 0 . . 0 . . . 0 0 .} {0 . . . . . . 0 0 . . . 0 . . 0} {. . . 0 0 . . . . . . 0 0 . . 0} {. . 0 . . 0 . . . . 0 . . 0 0 .} {. . 0 . . 0 . . . 0 0 . . 0 . .} {. . . 0 0 . . . 0 . . 0 0 . . .} {0 . . . . . . 0 0 . . 0 . . . 0} {. 0 . . . . 0 . . 0 0 . . . 0 .}} Now Simplify is NEVER going to recognize this pattern and produce something dramatically simpler. But I think that if you stare at the k-map for a while you might be able to come up with a much simpler expression than you started with. I didn't expect to have this much luck with this. I swapped an email or two with the original poster and his real problem is far larger than this. But with this promising start I think he might have a non-zero chance with his problem now. Note: Hasn't anyone written Karnaugh Map functions for Mathematica? I googled around for Mathematica logic reduction stuff and had no success.