13th International Conference on Membrane Computing - MTA Sztaki

On efficient algorithms for SAT
2.4 Symport/antiport Systems
The SAT is also solved by symport/antiport systems using membrane division
by an alphabet of size approximately 11k + 2km + (9k + m + k log m) log(9k +
m + k log m). The details of this algorithm can be seen in [1].
2.5 Minimal Parallelism and Membrane Divisions
The SAT is also solved effectively by membrane systems with minimal parallelism.
P systems constructed in a uniform manner and working in the minimally
parallel mode using non-cooperative rules, non-elementary membrane divisions,
move in and out rules and label changing can solve SAT in linear time. The size
of the used alphabet is larger than 4mk + 13k + 2m. Similar models are used
to solve SAT in linear time with respect to the number of the variables and
the number of clauses: P systems constructed in a uniform manner, working in
the minimally parallel mode using cooperative rules, non-elementary membrane
divisions, and move in and out rules solve SAT in linear time. Similarly, P systems
working in the minimally parallel mode with cooperative rules, elementary
membrane divisions and move out rules solve SAT in linear time; moreover they
are constructed in a semi-uniform manner in [13].
The satisfiability of any propositional formula in CNF can be decided in
a linear time with respect to k by a P system with active membranes using
object evolution, move in and out rules, membrane dissolution and division; and
working in the minimally parallel mode. Moreover, the system is constructed in
a linear time with respect to k and m in a semi-uniform way [6]. This method
uses an alphabet of size 7k + m + 11.
The n-SAT can be solved by recognizing P systems with active membranes
operating under minimal parallelism without polarities, and using evolution
rules, move in and out rules, membrane division and membrane creation. The P
system requires exponential space and linear time [9]. Here the size of the used
alphabet is larger than 5k + 4m.
In [2] polarity is also used. Here the parameter l refers for the number of
occurrences of literals in the formula (with multiplicities). A uniform family of P
systems with evolution rules, move out rules and membrane divisions; working
in minimally parallel way can solve SAT with four polarizations in a quadratic
number (i.e., (l(m+n))) of steps. The size of the alphabet is larger than 4km(k+
m) + 2l(m + k) + 2kl + m + k + k(4l + 3) + m(4l + 1).
2.6 Membrane Systems with String Objects
In [33] there is a method for SAT that uses string replication (replicated rewriting).
The process uses approximately 4k kinds of objects in the alphabet and
solves the problem in k + m + 1 steps.
2.7 P Systems with Contextual Rules
In [16] the SAT is solved in linear time by one-sided contextual rules using an
alphabet of size 3k + m + 2.
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