Is minimization of boolean expressions NP-Complete?

Question

I know that boolean satisfiability is NP-Complete, but is the minimization/simplification of a boolean expression, by which I mean taking a given expression in symbolic form and producing an equivalent but simplified expression in symbolic form, NP-Complete? I'm not sure that there's a reduction from satisfiability to minimization, but I feel like there probably is. Does anyone know for sure?

Answer 1

Well, look at it this way: using a minimizing algorithm, you can compact any non-satisfiable expression to the literal false, right? This effectively solves SAT. So at least a complete minimizing algorithm is bound to be NP-complete NP hard.