math - How to solve this type of equations automatically? -

math - How to solve this type of equations automatically? -

i.e.

x = z + (x^y)v(x^z) y = z + (x^z) z = (x^y)

think x, y, z 8-bits number in these equations, means add together operation occur carry in.

is there programme or algorithm can solve these equations programmatically ?

advances, if bring shift opration equations ? suppose alter sec equation to

y = z + (x^z)<<<5

more serious,

y = z + (x^z)<<<x

is possible solve programmatically ? if not, how solve hands?

thanks.

have @ boolean satisfiability problem. set of boolean equations can reduced single normal form look (a v b v ... v c) ^ (x v y v ... v z). bsat problem asks if there set of boolean values mean look evaluates true. in computational terms np-complete problem, take lot computing powerfulness solve expressions involving lots of variables. there programs lower downwards page can solve problem big set of values.

if number of variable have little simplest brute-force algorithm. seek every possibility. if have n variables there 2^n sets of values try. if n=10 thats 1024 sets test done in blink of eye.

without + or shift operators treat equations bitwise, x=(x1,x2,x3,x4,x5,x6,x7,x8) giving 1 set of equations each set of bits, solve independently. adding + , shift create things bit more complex still set of bitwise equations. 3 variables brute-force still reasonable 2^24 =16,777,216 sets seek solved in sec on modern hardware. 4 variables take 256 times long , 5 variables starts getting slow.

math equation boolean-logic