Open Problems in Membrane Computing and How Not to Solve Them

Leporati, Alberto; Manzoni, Luca; Mauri, Giancarlo; Porreca, Antonio E.; Zandron, Claudio

doi:10.1007/978-3-030-00265-7_15

Cited by 1 publication

(1 citation statement)

References 14 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…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].…”

Section: Discussionmentioning

confidence: 99%

P systems with proteins: a new frontier when membrane division disappears

et al. 2019

View full text Add to dashboard Cite

P systems with active membranes are usually defined as devices hierarchically structured that evolve through rewriting rules. These rules take the inspiration on the chemical reactions that happen within a cell and the role of both the inner and the plasma membranes as a "filter", letting components pass or not. Classically, these systems are non-cooperative, that is, the left-hand side of the rules has at most one object. Using polarizations, dissolution or cooperation, these systems have been proved to have enough power to efficiently solve computationally hard problems, obtaining new complexity frontiers with respect to their non-cooperative counterparts. In this paper, division rules are interchanged by separation rules. While the first ones produce two new membranes and two new objects, duplicating the objects within the original one, separation rules distribute the objects of the original membrane into the two new created membranes, so no new objects are created in this way. To obtain new objects, a rule of the type [ a → a 2 ] would be needed to accomplish that feature that seems to be necessary to obtain efficient solutions to NP-complete problems. Here, we present the limits when using separation rules instead of division rules.

show abstract