74 research outputs found
On the Computational Power of Spiking Neural P Systems
In this paper we study some computational properties of spiking neural P
systems. In particular, we show that by using nondeterminism in a slightly extended
version of spiking neural P systems it is possible to solve in constant time both the
numerical NP-complete problem Subset Sum and the strongly NP-complete problem
3-SAT. Then, we show how to simulate a universal deterministic spiking neural P system
with a deterministic Turing machine, in a time which is polynomial with respect to the
execution time of the simulated system. Surprisingly, it turns out that the simulation
can be performed in polynomial time with respect to the size of the description of the
simulated system only if the regular expressions used in such a system are of a very
restricted type
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
Time-driven computations in P Systems
It is a well-known fact that the time of execution of a (biochemical) reaction
depends on many factors, and, in particular, on the current situation of the whole system.
With this motivation in mind, we propose a model of computation based on membrane
systems where the various rewriting rules have different times of execution and, moreover,
the time of execution of each rule can vary during the computation, depending on the
configuration of the whole system (in this sense, the computation is "time-driven"). We
show that such systems are universal in a very simple framework: a regular time-mapping
suffices to obtain universality for systems with minimal cooperation (one catalyst)
Non-confluence in divisionless P systems with active membranes
AbstractWe describe a solution to the SAT problem via non-confluent P systems with active membranes, without using membrane division rules. Furthermore, we provide an algorithm for simulating such devices on a nondeterministic Turing machine with a polynomial slowdown. Together, these results prove that the complexity class of problems solvable non-confluently and in polynomial time by this kind of P system is exactly the class NP
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
Dynamical Probabilistic P Systems: Definitions and Applications
We introduce dynamical probabilistic P systems, a variant where probabilities associated to the rules change during the evolution of the system, as a new approach
to the analysis and simulation of the behavior of complex systems. We define the notions
for the analysis of the dynamics and we show some applications for the investigation of the
properties of the Brusselator (a simple scheme for the Belousov-Zabothinskii reaction),
the Lotka-Volterra system and the decay process
On a Paun’s Conjecture in Membrane Systems
We study a P˘aun’s conjecture concerning the unsolvability of
NP–complete problems by polarizationless P systems with active membranes
in the usual framework, without cooperation, without priorities,
without changing labels, using evolution, communication, dissolution and
division rules, and working in maximal parallel manner. We also analyse
a version of this conjecture where we consider polarizationless P systems
working in the minimally parallel manner.Ministerio de Educación y Ciencia TIN2006–13425Junta de Andalucía TIC–58
Complexity aspects of polarizationless membrane systems
We investigate polarizationless P systems with active membranes working in
maximally parallel manner, which do not make use of evolution or communication rules, in
order to find which features are sufficient to efficiently solve computationally hard problems.
We show that such systems are able to solve the PSPACE-complete problem
QUANTIFIED 3-SAT, provided that non-elementary membrane division is controlled by the
presence of a (possibly non-elementary) membrane.Ministerio de Educación y Ciencia TIN2006-13425Junta de Andalucía TIC-58
Size and Power of Extended Gemmating P Pystems
In P systems with gemmation of mobile membranes were ex-
amined. It was shown that (extended) systems with eight membranes are as
powerful as the Turing machines. Moreover, it was also proved that extended
gemmating P systems with only pre-dynamical rules are still computationally
complete: in this case nine membranes are needed to obtain this computational
power. In this paper we improve the above results concerning the size bound
of extended gemmating P systems, namely we prove that these systems with
at most ¯ve membranes (with meta-priority relations and without (in=out)
communication rules) form a class of universal computing devices, while in
the case of extended systems with only pre-dynamical rules six membranes are
enough to determine any recursively enumerable language
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