list manipulation - Converting truth tables to boolean expressions

I have a truth table for a Boolean expression represented like this

table={{0, 0, 0, 0} -> 0, {0, 0, 0, 1} -> 0, {0, 0, 1, 0} -> 

0, {0, 0, 1, 1} -> 0, {0, 1, 0, 0} -> 0, {0, 1, 0, 1} -> 
0, {0, 1, 1, 0} -> 0, {0, 1, 1, 1} -> 1, {1, 0, 0, 0} -> 
1, {1, 0, 0, 1} -> 1, {1, 0, 1, 0} -> 1, {1, 0, 1, 1} -> 
1, {1, 1, 0, 0} -> 1, {1, 1, 0, 1} -> 1, {1, 1, 1, 0} -> 
1, {1, 1, 1, 1} -> 0}

(all on one line)

The table contains the values I want at the output given y4,y3,y2,y1 at the input, i.e.

{y4,y3,y2,y1} -> desiredOutput

What is the best way to transform this data into a form that can be then processed in terms of y with functions such as BooleanMinimize?

Answer

BooleanMinimize[BooleanFunction[table]]

(*  (#1 && ! #2) || (#1 && ! #3) || (#1 && ! #4) || (! #1 && #2 && #3 &&  #4) & *)

Note in the documentation how 1/0 vs True/False are treated here, massage as needed.

Quick verification:

bf = BooleanFunction[table];


Rule @@@ Transpose[{table[[All, 1]], 
    bf[Sequence @@ #] & /@ table[[All, 1]] // Boole}];

% == table

(* True *)

Comments

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