Petri net algorithms in the theory of matrix grammars
Acta Informatica
Order parameter for a symbolic chemical system
ALIFE Proceedings of the sixth international conference on Artificial life
Membrane computing with external output
Fundamenta Informaticae
Journal of Computer and System Sciences
P systems with active membranes: attacking NP-complete problems
Journal of Automata, Languages and Combinatorics
Computing with cells and atoms: an introduction to quantum, DNA and membrane computing
Computing with cells and atoms: an introduction to quantum, DNA and membrane computing
Handbook of Formal Languages
Regulated Rewriting in Formal Language Theory
Regulated Rewriting in Formal Language Theory
Mathematical Theory of L Systems
Mathematical Theory of L Systems
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
From regulated rewriting to computing with membranes: collapsing hierarchies
Theoretical Computer Science
Languages generated by P systems with active membranes
New Generation Computing - Membrane computing
P Systems with Mobile Membranes
Natural Computing: an international journal
A Biologically Inspired Model with Fusion and Clonation of Membranes
UC '08 Proceedings of the 7th international conference on Unconventional Computing
Uniform solution of QSAT using polarizationless active membranes
MCU'07 Proceedings of the 5th international conference on Machines, computations, and universality
Characterizing membrane structures through multiset tree automata
WMC'07 Proceedings of the 8th international conference on Membrane computing
On the verification of membrane systems with dynamic structure
Natural Computing: an international journal
Identifying p rules from membrane structures with an error-correcting approach
WMC'06 Proceedings of the 7th international conference on Membrane Computing
Editing distances between membrane structures
WMC'05 Proceedings of the 6th international conference on Membrane Computing
An approach to computational complexity in membrane computing
WMC'04 Proceedings of the 5th international conference on Membrane Computing
The power of mobility: four membranes suffice
CiE'05 Proceedings of the First international conference on Computability in Europe: new Computational Paradigms
On efficient algorithms for SAT
CMC'12 Proceedings of the 13th international conference on Membrane Computing
Time-free solution to SAT problem using P systems with active membranes
Theoretical Computer Science
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First, we consider P systems with active membranes, hence with the possibility that the membranes can be divided, with non-cooperating evolution rules (the objects always evolve separately). These systems are known to be able to solve NP-complete problems in linear time. Here we give a normal form theorem for such systems: their computational universality is preserved even if only the elementary membranes are divided. The possibility of solving SAT in linear time is preserved only when non-elementary membranes may also be divided under the influence of objects in their region.Second, we consider a slight generalization, namely, we allow that a membrane can produce by division both a copy of itself and a copy of a membrane with a different label; again, only elementary membranes may be divided. In this case, we prove that the hierarchy on the maximal number of membranes present in the system collapses: three membranes at a time are sufficient in order to characterize the recursively enumerable sets of vectors of natural numbers. This result is optimal, two membranes are shown not to be sufficient.Third, we consider P systems with cooperating rules (several objects may evolve together). Making use of this powerful feature, we show that many NP-complete problems can be solved in linear time in a quite uniform way (by systems which are very similar to each other), using only elementary membranes division (and not further ingredients, such as electrical charges). The degree of cooperation is minimal: two objects at a time.