13th International Conference on Membrane Computing - MTA Sztaki

B. Nagy
2.8 Neural-like Membrane Systems
Neural-like membrane systems (or tissue P systems) can solve SAT in linear
time by using an alphabet of chemical objects (or excitations/impulses) with
cardinality 2 k+1 −1 [34], since the system first generates all the truth-assignments
in the form of strings of length k using letters t i and f i with 1 ≤ i ≤ n.
2.9 Quantum P-systems
In this section we recall a mixed paradigm, the quantum UREM P-systems [19].
Quantum computing is also counted as a new computing paradigm based on some
‘unconventional’ features of quantum mechanics. There is no space here to recall
all details, there are various textbooks for this topic also (see, e.g., [11]). The
main features of this paradigm are the following. A quantum bit (qubit) can have
infinitely many values, technically any unit vector of a four dimensional space
(complex coefficients for both of the possible values |0〉 and |1〉), the quantum
superposition of the two possible states. The used unitary operations (rotations)
can be written by 2 by 2 (complex valued) matrices. However by measurement
only the ‘projection’ of the superposition is obtained, the system reaches one of
the states |0〉 and |1〉 with the probability based on their coefficients. Having
a system with n qubits the dimension of its state (i.e., the stored information)
grows exponentially: the state can be described by a 2 n dimensional vector.
The corresponding operators are described by matrices of size 2 n by 2 n (can be
obtained by tensor product). By special quantum effect, called entanglement,
a state in superposition of some qubits together may not be constructible by
the tensor products of the qubits. In this way exponential ‘space’ can be used.
(Theoretically it is nice, technologically it is very hard task to produce systems
that can use larger (e.g., 30) number of qubits in a system.)
In UPREM P-systems there are unit rules and energy assigned to membranes.
The rules in these systems are applied in a sequential way: at each computation
step, one rule is selected from the pool of currently active rules, and it is applied.
The system further developed by mixing it with quantum computing. Quantum
UPREM P-systems are proved to be universal without priority relation among
the rules [18]. In this way, a quantum computing technique: solution to SAT by
the quantum register machine is simulated. The given semi-uniform algorithm
uses the alphabet to describe the possible quantum states, and as the number
of possible states of the system is exponential on the number of used qubits, the
size of the alphabet is exponential on the input formula.
2.10 Mutual Mobile Membrane Systems
In mutual mobile membrane systems endocytosis and exocytosis work whenever
the involved membranes ‘agree’ on the movement. Actually, in [4] only weak NPcomplete
problems, i.e., the knapsack, the subset-sum and the 2-partition are
solved and our main problem, the strong NP-complete SAT does not. However,
this branch of P-systems seems to be interesting and therefore we decided to
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