Re: Evaluation of boolean functions in Mathematica 8

*To*: mathgroup at smc.vnet.net*Subject*: [mg127568] Re: Evaluation of boolean functions in Mathematica 8*From*: Dana DeLouis <dana2010 at me.com>*Date*: Sat, 4 Aug 2012 21:45:55 -0400 (EDT)*Delivered-to*: l-mathgroup@mail-archive0.wolfram.com*Delivered-to*: l-mathgroup@wolfram.com*Delivered-to*: mathgroup-newout@smc.vnet.net*Delivered-to*: mathgroup-newsend@smc.vnet.net

Thank you Bob for the excellent suggestions. I've never used Grid before, so I got side-tracked on learning about this function. I know there are many variations one can do along this theme. So, here's a variation that incorporated some of your ideas. I added a column that attempts to find a simpler version if it finds one. What is considered simpler is of course subjective, so this is only an attempt. :>) // ===== Main Function ===== TruthTable[equ_,steps_List:{}]:=Module[{v,data,min,hdg}, v = BooleanVariables[equ]; AppendTo[v,{steps,equ}]; (* If shorter version found, add that to the end *) min=BoolMin[equ]; If[UnsameQ[min,equ],AppendTo[v,min]]; v=Flatten[v]; (* Calculate table *) data=BooleanTable[v]; (* Adjust Table Data *) data = data/.{True->Style["T",Blue,Bold],False->Style["F",LightGray]}; (* Add Ref numbers *) data=Join[Map[List,Range[Length[data]]],data,2]; (* Add 2 Heading Rows *) hdg = Join[{"#"},v]; PrependTo[data,Style[TraditionalForm[#],Bold]&/@hdg]; PrependTo[data,hdg]; data =ReplacePart[data,{1,1}->""]; Grid[data, Frame->All, Alignment->Center, ItemSize->Automatic, Background -> {None,{LightBlue,LightBlue},{{{3,-1},{-1,-1}}->LightYellow}} ] ] // ===== Aux functions ===== // Note: Physically try each of the Form Options, and pick the shortest LeafCount. // If there's a tie with original equation, return original equation. BoolMin[equ_]:=Module[{opts,v,len}, opts = {"DNF","SOP","CNF","POS","ANF","NOR","NAND","AND","OR"} ; v=BooleanMinimize[equ,#]&/@opts; (* Place Original equation at beginning of list *) PrependTo[v,equ]; len=LeafCount/@v; First[Pick[v,len,Min[len]]] ] // ===== End of Functions ===== // Simple equ=And[p,q,r]; TruthTable[equ] // If you want to see the intermediate step of And[x,y], add it to the list. equ=Not[Or[And[x,y],z]]; TruthTable[equ, {And[x,y]} ] // This is a longer equation. The last column suggests a simpler version without d. // Both columns are printed so as to visually confirm this. equ=And[And[Xor[a,b],c],Xor[a,c],Or[c,d]]; TruthTable[equ] Again, there are lots of variations along this theme. I like having TraditionalForm in the title at least for now. This way, I can learn the symbols that I don't use often. Thank you for your suggestions. Interesting subject. :>) = = = = = = Dana DeLouis Mac & Math 8 = = = = = = On Aug 1, 4:57 am, lalwani.ak... at gmail.com wrote: > Hello, > > I want to evaluate a Boolean function by substituting True and False values for its variables, to get a True or False value at the output. Example, > > g = BooleanConvert[And[p, q, r], "BFF"] > > g[True,True,True] > > But the above statement does not evaluate g at the data-point given, but instead returns the statement, > > BooleanFunction[<3>][p,q,r][True,True,True] > > Can anybody please suggest how to proceed? > > Thanks a lot.