2019 **Abstract:** In the field of membrane computing, a great attention is traditionally paid to the results demonstrating a theoretical possibility to solve NP-complete problems in polynomial time by means of various models of P systems. A bit less common is the fact that almost all models of P systems with this capability are actually stronger: some of them are able to solve PSPACEcomplete problems in polynomial time, while others have been recently shown to characterize the class # (which is conjectured to be strictly includ…

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“…Several results in other frameworks comparing division rules and separation rules lead one to believe that not only an exponential workspace in terms of membranes is sufficient, but also that it has to go along with exponential workspace in terms of objects to solve computationally hard problems efficiently [13,29,30,32]. Some interesting research lines are given by the open problems stated in [25], such as the role of the ability to change the proteins in a rule while using division rules, or allowing division only for elementary membranes, as well as in another publications [12,18].…”

confidence: 99%

“…Several results in other frameworks comparing division rules and separation rules lead one to believe that not only an exponential workspace in terms of membranes is sufficient, but also that it has to go along with exponential workspace in terms of objects to solve computationally hard problems efficiently [13,29,30,32]. Some interesting research lines are given by the open problems stated in [25], such as the role of the ability to change the proteins in a rule while using division rules, or allowing division only for elementary membranes, as well as in another publications [12,18].…”

confidence: 99%

“…In Sect. 4, an answer to the problem stated in [25] is given. The paper is closed with some conclusions and defining future research lines.…”

confidence: 99%

“…For recent results on this subject, we refer the reader to [4,[19][20][21]26]. A survey on different strategies to go beyond in the framework of P systems can be found in [42].…”

confidence: 99%

“…Furthermore, Petri nets with localities were also used to describe membrane creation and membrane dissolution in [8] and extended in [7] to model the use of promoters and inhibitors. For more details on the specific membrane system models and their computational power, see the handbook [14,20,21] for more recent developments. On the connections of these models to variants of Petri nets with localities, the reader is also referred to [14].…”

confidence: 99%