2
votes
1answer
53 views

How to prove that linear functions cannot represent binary functions

Yesterday, I thought about representing boolean algebra as linear functions: For some vector space $V$ and for some $A, B \subset V$ such that $A \ne \emptyset \,\wedge\, B \ne \emptyset ...
1
vote
1answer
45 views

boolean algebra simplyfing

I need to solve these expressions with boolean algebra: $$Z = a'bc+ab'c+abc'+abc\mbox{ AND }Z = a'(b+db'c')+a'b'(d'c'+c)$$ Every advice is more then welcome. Thanks
3
votes
1answer
194 views

Solving special boolean equation set

I have boolean equation sets that look like this (where ^ means xor): eq 1: x1^x3^x5^x6^x9^x10^x11^x13^x17^x18 = 0 eq 2: 1^x1^x3^x10^x12^x17 = 0 eq 3: 1^x2^x3^x5^x8^x10^x14^x16 = 0 ...
0
votes
0answers
23 views

Can matrices be reduced in the same way that Karnaugh maps can be expressed as an equation?

I'm doing linear algebra, and boolean algebra for electronics and I'm wondering if there are any standard mathematical ways in linear to express a matrix more simply without resulting to graphical ...
0
votes
2answers
421 views

Boolean Algebra A + AB = A

Hi I have a question about the following algebra rule A + AB = A My textbook explains this as follows A + AB = A This rule can be proved as such: Step 1: Dustributive Law: A + AB = A*1 = A(1+B) ...
0
votes
0answers
128 views

Given a state transformation matrix and a state vector, how to find the total number of changes for each individual element.

I have a vector of binary variables, $s$ representing a state at some point in time, and a transformation matrix $T$. The initial state is $s_0$. $s_n = Ts_{n-1}$ Given a number of transformations, ...
0
votes
1answer
60 views

Number of basis representations of Boolean vectors

Suppose I have a basis $v_1, ..., v_n$ of boolean vectors and a boolean vector $v$ that was constructed by iterated $v = v_i$ $OR$ $v_j$ statements. I want a way to figure our how many unique ...
4
votes
6answers
2k views

how to solve system of linear equations of XOR operation?

how can i solve this set of equations ? to get values of $x,y,z,w$ ? $$\begin{aligned} 1=x \oplus y \oplus z \end{aligned}$$ $$\begin{aligned}1=x \oplus y \oplus w \end{aligned}$$ $$\begin{aligned}0=x ...
1
vote
1answer
148 views

Find an optimal 4-tuple which satisfies a boolean expression

(I have post a question with bounty for several days (Find a best 4-tuple which fulfils a variable boolean formula), but unfortunately got no answer yet. Here I simplify it to a smaller problem and ...
1
vote
1answer
351 views

How many presentable boolean functions with n attributes are linear separable?

The aim is to find a formula for the question. For n=2 i get (2^(2^n)=16 possible functions. This is the solution for a boolean function with 2 attributes: ...