Mobile Membranes: Computability and Complexity

P Systems Implementation: A Model of Computing for Biological Mitochondrial Rules using Object Oriented Programming

“…The efficient variants of Membrane systems and the formal definitions of P systems are investigated from computational complexity theory [34]. Elegant works for NP-complete problems such as Boolean Satisfiability (SAT) problem, has been shown with the polynomial solutions with active membrane principles [26,16], The Hamiltonian Cycle Problem (HCP) [37], and Travelling Salesman Problem (TSP) [38]. SAT solution is also set by P systems with active membranes by division rule for elementary membranes without dissolution rule.…”

“…These rules had restrictions that created an exponential workspace in membranes terms in polynomial time, not in objects [41,42]. The Turing completeness is achieved by using elementary division rules for nine membranes [16,43]. Used a combination of division, mexo and mendo behaviors to achieve the final configuration.…”

“…According to these phenomena, the framework of active membranes in polarizationless P systems [14] are developed and evaluated by using rewriting rules [7] which can be merged, divided, separated, or passed through membranes [15]. Another variant of cell-like P system was inspired by cells movement as exocytosis and endocytosis rules that are expressed of the outside and inside processes of neighboring membranes, this variant is called mobile membranes [16]. www.ijacsa.thesai.org A general form of cell-like P systems variants is shown in Fig.…”

Mobile Membranes

“…Theorem 5 [19]: By using mobile membrane systems with the rules mendo, mexo and ediv, SAT can be solved in a polynomial number of steps.…”