First lets say you have an input vector and an output vector describing states. Let us use a binary number system, it doesn't really matter for mathematics.

Say, I have an input vector V, components v_i. Now I would like to have an output vector W which can be of other dimension. The allowed mathematical relations between the input components are AND, OR, XOR, NOT for example.

Let me write one example:

w_2 = 1 if ((v_1 AND NOT v_2) OR (NOT v_1 AND v_3) else 0

I thought about some simple transition matrix

W = A1 * V

but as it seems to me the OR (or XOR) is the killer, it makes the system of equations nonlinear, right?

The question finally is: How can I write down code with not that many logical implications but using logical matrices... not sure... thanks for a hint!