P systems with active membranes: attacking NP-complete problems
Journal of Automata, Languages and Combinatorics
Handbook of Formal Languages
Regulated Rewriting in Formal Language Theory
Regulated Rewriting in Formal Language Theory
Membrane Computing: An Introduction
Membrane Computing: An Introduction
P Systems with Gemmation of Mobile Membranes
ICTCS '01 Proceedings of the 7th Italian Conference on Theoretical Computer Science
On the power of membrane division in P systems
Theoretical Computer Science - Words, languages and combinatorics
Rewriting P systems: improved hierarchies
Theoretical Computer Science
Further Results on Contextual and Rewriting P Systems
Fundamenta Informaticae - Contagious Creativity - In Honor of the 80th Birthday of Professor Solomon Marcus
On the efficiency of p systems with active membranes and two polarizations
WMC'04 Proceedings of the 5th international conference on Membrane Computing
Universality results for P systems based on brane calculi operations
Theoretical Computer Science
Describing the Immune System Using Enhanced Mobile Membranes
Electronic Notes in Theoretical Computer Science (ENTCS)
Editing Configurations of P Systems
Fundamenta Informaticae
Engineering Societies in the Agents World VIII
On the Computational Power of Enhanced Mobile Membranes
CiE '08 Proceedings of the 4th conference on Computability in Europe: Logic and Theory of Algorithms
Membrane computing with transport and embedded proteins
Theoretical Computer Science
Turing Completeness Using Three Mobile Membranes
UC '09 Proceedings of the 8th International Conference on Unconventional Computation
On the reachability problem in P systems with mobile membranes
WMC'07 Proceedings of the 8th international conference on Membrane computing
OPERASCC: an instance of a formal framework for MAS modeling based on population P systems
WMC'07 Proceedings of the 8th international conference on Membrane computing
Mobility in computer science and in membrane systems
CMC'10 Proceedings of the 11th international conference on Membrane computing
An overview of membrane computing
ICDCIT'11 Proceedings of the 7th international conference on Distributed computing and internet technology
Upper and lower bounds for the computational power of p systems with mobile membranes
CiE'06 Proceedings of the Second conference on Computability in Europe: logical Approaches to Computational Barriers
Editing Configurations of P Systems
Fundamenta Informaticae
On the computability power of membrane systems with controlled mobility
CiE'12 Proceedings of the 8th Turing Centenary conference on Computability in Europe: how the world computes
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P systems with active membranes are among the central ones in membrane computing, and they were shown to be both computationally universal (able to simulate Turing machines) and computationally efficient (able to solve hard problems in polynomial time). However, in all cases, these results were obtained by making use of several powerful features, such as membrane polarization, label changing, division of non-elementary membranes, priorities, or cooperative rules. This paper contributes to the research effort of introducing a class of P systems with active membranes having none of the features mentioned above, but still preserving the power and the efficiency. The additional feature we consider instead are the operations of endocytosis and exocytosis: moving a membrane inside a neighboring membrane, or outside the membrane where it is placed. We investigate the power and the efficiency of these systems (also using membrane division) by first proving that they can simulate (with a linear slowdown and without introducing non-determinism) rewriting P systems with 2-replication, for which the universality and the possibility of solving NP-complete problems in polynomial time are known. In this way, the universality and efficiency are also obtained for our systems. We also give a direct and simple proof for the universality result --- without using division rules (the proof uses nine membranes, but we do not know whether this number can be decreased).