In the present paper we propose a way to simulate Boolean gates and circuits in the framework of P systems with active membranes using inhibiting/de-inhibiting rules. This new approach on the simulation of Boolean gates has the advantage of a self-embedded synchronization, an extra system to solve this problem not being needed. Moreover, the number of membranes and objects we use for the Boolean gates simulation is only two. NP-complete problems, particularly CIRCUIT-SAT, were also considered here. In addition, we propose a ‘DNA-like’ way of solving SAT problem using the tools given by merging and separation operations in P systems.