168 research outputs found
Characterizing PSPACE with Shallow Non-Confluent P Systems
In P systems with active membranes, the question of understanding the
power of non-confluence within a polynomial time bound is still an open problem. It is
known that, for shallow P systems, that is, with only one level of nesting, non-con
uence
allows them to solve conjecturally harder problems than con
uent P systems, thus reaching PSPACE. Here we show that PSPACE is not only a bound, but actually an exact
characterization. Therefore, the power endowed by non-con
uence to shallow P systems
is equal to the power gained by con
uent P systems when non-elementary membrane
division and polynomial depth are allowed, thus suggesting a connection between the
roles of non-confluence and nesting depth
Characterizing PSPACE with Shallow Non-Confluent P Systems
In P systems with active membranes, the question of understanding the
power of non-confluence within a polynomial time bound is still an open problem. It is
known that, for shallow P systems, that is, with only one level of nesting, non-con
uence
allows them to solve conjecturally harder problems than con
uent P systems, thus reaching PSPACE. Here we show that PSPACE is not only a bound, but actually an exact
characterization. Therefore, the power endowed by non-con
uence to shallow P systems
is equal to the power gained by con
uent P systems when non-elementary membrane
division and polynomial depth are allowed, thus suggesting a connection between the
roles of non-confluence and nesting depth
Improving Universality Results on Parallel Enzymatic Numerical P Systems
We improve previously known universality results on enzymatic numerical
P systems (EN P systems, for short) working in all-parallel and one-parallel modes. By
using a
attening technique, we rst show that any EN P system working in one of these
modes can be simulated by an equivalent one-membrane EN P system working in the
same mode. Then we show that linear production functions, each depending upon at most
one variable, su ce to reach universality for both computing modes. As a byproduct, we
propose some small deterministic universal enzymatic numerical P systems
Simulating counting oracles with cooperation
We prove that monodirectional shallow chargeless P systems with active
membranes and minimal cooperation working in polynomial time precisely characterise
P#P
k , the complexity class of problems solved in polynomial time by deterministic
Turing machines with a polynomial number of parallel queries to an oracle for a counting
problem
Complete Problems for a Variant of P Systems with Active Membranes
We identify a family of decision problems that are hard for some complexity
classes defined in terms of P systems with active membranes working in polynomial time.
Furthermore, we prove the completeness of these problems in the case where the systems
are equipped with a form of priority that linearly orders their rules. Finally, we highlight
some possible connections with open problems related to the computational complexity
of P systems with active membranes
Introducing a Space Complexity Measure for P Systems
We define space complexity classes in the framework of membrane computing, giving some initial results about their mutual relations and their connection with time
complexity classes, and identifying some potentially interesting problems which require
further research
Monodirectional P Systems
We investigate the in
uence that the
ow of information in membrane systems
has on their computational complexity. In particular, we analyse the behaviour of P systems
with active membranes where communication only happens from a membrane towards
its parent, and never in the opposite direction. We prove that these \monodirectional
P systems" are, when working in polynomial time and under standard complexity-theoretic
assumptions, much less powerful than unrestricted ones: indeed, they characterise classes
of problems de ned by polynomial-time Turing machines with NP oracles, rather than
the whole class PSPACE of problems solvable in polynomial space
A Toolbox for Simpler Active Membrane Algorithms
We show that recogniser P systems with active membranes can be
augmented with a priority over their set of rules and any number of membrane
charges without loss of generality, as they can be simulated by standard P systems
with active membranes, in particular using only two charges. Furthermore, we
show that more general accepting conditions, such as sending out several, possibly
contradictory results and keeping only the first one, or rejecting by halting without
output, are also equivalent to the standard accepting conditions. The simulations
we propose are always without significant loss of efficiency, and thus the results of
this paper can hopefully simplify the design of algorithms for P systems with active
membranes
Subroutines in P Systems and Closure Properties of Their Complexity Classes
The literature on membrane computing describes several variants of P systems
whose complexity classes C are "closed under exponentiation", that is, they satisfy
the inclusion PC C, where PC is the class of problems solved by polynomial-time
Turing machines with oracles for problems in C. This closure automatically implies closure
under many other operations, such as regular operations (union, concatenation,
Kleene star), intersection, complement, and polynomial-time mappings, which are inherited
from P. Such results are typically proved by showing how elements of a family of
P systems can be embedded into P systems simulating Turing machines, which exploit
the elements of as subroutines. Here we focus on the latter construction, abstracting
from the technical details which depend on the speci c variant of P system, in order to
describe a general strategy for proving closure under exponentiation
Determination of endogenous and exogenous corticosteroids in bovine urine and effect of fighting stress during the "Batailles des Reins" on their biosynthesis
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