3,191 research outputs found
P Systems with Active Membranes and Without Polarizations
P systems with active membranes but without using electrical charges
(polarizations) are shown to be complete for generating recursively enumerable string
languages when working on string objects and using only rules with membrane transitions as well as rules with membrane dissolving and elementary membrane division,
but also when using various other kinds of rules, even including a new type of rules allowing for membrane generation. Especially, allowing for changing membrane labels
turns out to be a very powerful control feature
P Systems with Active Membranes, Without Polarizations and Without Dissolution: A Characterization of P
We study the computational efficiency of recognizer P systems
with active membranes without polarizations and without dissolution.
The main result of the paper is the following: the polynomial
computational complexity class associated with the class of recognizer P
systems is equal to the standard complexity class P.Ministerio de Ciencia y Tecnología TIC2002-04220-C03-0
Polarizationless P Systems with One Active Membrane
The aim of this paper is to study the computational power of P systems with
one active membrane without polarizations. For P systems with active membranes, it is
known that computational completeness can be obtained with either of the following combinations
of features: 1)two polarizations, 2)membrane creation and dissolution, 3)four
membranes with three labels, membrane division and dissolution, 4)seven membranes
with two labels, membrane division and dissolution.
Clearly, with one membrane only object evolution rules and send-out rules are permitted.
Two variants are considered: external output and internal output
On the Power of Dissolution in P Systems with Active Membranes
In this paper we study membrane dissolution rules in the
framework of P systems with active membranes but without using electrical
charges. More precisely, we prove that the polynomial computational
complexity class associated with the class of recognizer P systems
with active membranes, without polarizations and without dissolution
coincides with the standard complexity class P. Furthermore, we demonstrate
that if we consider dissolution rules, then the resulting complexity
class contains the class NP.Ministerio de Ciencia y Tecnología TIC2002-04220-C03-0
Minimal Parallelism and Number of Membrane Polarizations
It is known that the satisfiability problem (SAT) can be efficiently solved by a uniform family of P systems with active membranes that have two polarizations working in a maximally parallel way. We study P systems with active membranes without non-elementary membrane division, working in minimally parallel way. The main question we address is what number of polarizations is sufficient for an efficient computation depending on the types of rules used.In particular, we show that it is enough to have four polarizations, sequential evolution rules changing polarizations, polarizationless non-elementary membrane division rules and polarizationless rules of sending an object out. The same problem is solved with the standard evolution rules, rules of sending an object out and polarizationless non-elementary membrane division rules, with six polarizations. It is an open question whether these numbers are optimal
Computational efficiency of dissolution rules in membrane systems
Trading (in polynomial time) space for time in the framework of membrane systems is not sufficient to
efficiently solve computationally hard problems. On the one hand, an exponential number of objects
generated in polynomial time is not sufficient to solve NP-complete problems in polynomial time.
On the other hand, when an exponential number of membranes is created and used as workspace, the
situation is very different. Two operations in P systems (membrane division and membrane creation)
capable of constructing an exponential number of membranes in linear time are studied in this paper.
NP-complete problems can be solved in polynomial time using P systems with active membranes
and with polarizations, but when electrical charges are not used, then dissolution rules turn out to
be very important. We show that in the framework of P systems with active membranes but without
polarizations and in the framework of P systems with membrane creation, dissolution rules play a
crucial role from the computational efficiency point of view.Ministerio de Educación y Ciencia TIN2005-09345-C04-0
Polarizationless P Systems with Active Membranes Working in the Minimally Parallel Mode
We investigate the computing power and the efficiency of P systems with
active membranes without polarizations, working in the minimally parallel mode. We
prove that such systems are computationally complete and able to solve NP-complete
problems even when the rules are of a restricted form, e.g., for establishing computational
completeness we only need rules handling single objects and no division of non-elementary
membranes is usedMinisterio de Educación y Ciencia TIN2005-09345-C04-01Junta de Andalucía TIC 58
Recognizer P Systems with Antimatter
In this paper, we consider recognizer P systems with antimatter
and the in
uence of the matter/antimatter annihilation rules having weak
priority over all the other rules or not. We rst provide a uniform family of P
systems with active membranes which solves the strongly NP-complete problem
SAT, the Satis ability Problem, without polarizations and without dissolution,
yet with division for elementary membranes and with matter/antimatter annihilation
rules having weak priority over all the other rules. Then we show that
without this weak priority of the matter/antimatter annihilation rules over all
the other rules we only obtain the complexity class PMinisterio de Economía y Competitividad TIN2012-3743
One and Two Polarizations, Membrane Creation and Objects Complexity in P Systems
We improve, by using register machines, some existing universality results for specific models of P systems. P systems with membrane creation are known to generate all recursively enumerable sets of vectors of non-negative integers, even when no region (except the environment) contains more than one object of the same kind. We here show that they generate all recursively enumerable languages, and two membrane labels are sufficient (the same result holds for accepting all recursively enumerable vectors of non-negative integers). Moreover, at most two objects are present inside the system at any time in the generative case. Then we prove that 10 + m symbols are enough to generate any recursively enumerable language over m symbols. P systems with active membranes without polarizations are known to generate all recursively enumerable sets of vectors of non-negative integers. We show that they generate all recursively enumerable languages; four starting membranes with three labels or seven starting membranes with two labels are sufficient. P systems with active membranes and two polarizations are known to generate/accept all recursively enumerable sets of vectors of non-negative integers, only using rules of rewriting and sending objects out. We show that accepting can be done by deterministic systems. Finally, remarks and open questions are presented.Ministerio de Ciencia y Tecnología TIC2002-04220-C03-0
Membrane division, restricted membrane creation and object complexity in P systems
We improve, by using register machines, some existing universality results for specific models of
P systems. P systems with membrane creation are known to generate all recursively enumerable sets
of vectors of non-negative integers, even when no region (except the environment) contains more than
one object of the same kind.We showhere that they generate all recursively enumerable languages, and
that two membrane labels are sufficient (the same result holds for accepting all recursively enumerable
vectors of non-negative integers). Moreover, at most two objects are present inside the system at any
time in the generative case.We then prove that 10 + msymbols are sufficient to generate any recursively
enumerable language over m symbols. P systems with active membranes without polarizations are
known to generate all recursively enumerable sets of vectors of non-negative integers. We show that
they generate all recursively enumerable languages; four starting membranes with three labels or
seven starting membranes with two labels are sufficient. P systems with active membranes and two
polarizations are known to generate/accept all recursively enumerable sets of vectors of non-negative
integers, using only rules of rewriting and sending objects out.We show that accepting can be done by
deterministic systems. Finally, we show that P systems with restricted membrane creation (the newly
created membrane can only be of the same kind as the parent one) generate at least matrix languages,
even when having at most one object in the configuration (except the environment). We conclude by
presenting a summary of the main results obtained in this paper and a list of open questions.Ministerio de Ciencia y Tecnología TIC2002-04220-C03-0
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