Borderlines of efficiency: what’s up?

Abstract

Some of the theoretical open problems and current challenges concerning P systems from a theoretical perspective will be discussed, focusing on results related to searching bounds for computational com- plexity classes in general, and to the P vs NP problem and the P ̆aun’s conjecture in particular. Membrane computing is already a mature field, and the research commu- nity around it is becoming more interdisciplinary and diverse. Although nowadays it seems that practical applications receive a rapidly increasing attention, there are still key theoretical issues that need to be addressed