Is there a way to convert a program into a Boolean formula?

Question

Let's say I have a program P, in form of a binary code for x86 architecture.

I want to find a Boolean formula F (in form of CNF, or something like that), such that F(input,output) = true iff P(input) = output So to answer a question "what output does the program produce on given input" I will only need to run a SAT/SMT solver for X on formula F(input,X) == true. I understand that this problem is undecidable in general case, but I only care for some practical cases.

What keywords should I google to find more about this topic?