P Systems with Boundary Rules

Abstract

We propose a new variant of P Systems, based on boundary rules, shortly called PB Systems. Boundary rules means that rules are not internal to regions but theyare able to “see” even externally, that is, theyare sensible to what happens around the border of the membranes. We prove the computational universality for PB systems with three membranes which sense at most one symbol outside and one symbol inside a membrane. Finally, we investigate the relationships with the basic model of P systems by proving an equivalence between P systems without priority, thickness or dissolution operator, and PB systems that use communication rules of a restricted form.