问题
How to simplify a given boolean expression with many variables (>10) so that the number of occurrences of each variable is minimized?
In my scenario, the value of a variable has to be considered ephemeral, that is, has to recomputed for each access (while still being static of course). I therefor need to minimize the number of times a variable has to be evaluated before trying to solve the function.
Consider the function
f(A,B,C,D,E,F) = (ABC)+(ABCD)+(ABEF)
Recursively using the distributive and absorption law one comes up with
f'(A,B,C,E,F) = AB(C+(EF))
I'm now wondering if there is an algorithm or method to solve this task in minimal runtime.
Using only Quine-McCluskey in the example above gives
f'(A,B,C,E,F) = (ABEF) + (ABC)
which is not optimal for my case. Is it save to assume that simplifying with QM first and then use algebra like above to reduce further is optimal?
回答1:
Try Logic Friday 1
It features multi-level design of boolean circuits.
For your example, input and output look as follows:
回答2:
I usually use Wolfram Alpha for this sort of thing.
回答3:
You can use an online boolean expression calculator like https://www.dcode.fr/boolean-expressions-calculator
You can refer to Any good boolean expression simplifiers out there? it will definitely help.
来源：https://stackoverflow.com/questions/18474607/simplify-boolean-expression-i-t-o-variable-occurrence