730 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
First Steps Towards Linking Membrane Depth and the Polynomial Hierarchy
In this paper we take the first steps in studying possible connections between
non-elementary division with limited membrane depth and the levels of the Polynomial
Hierarchy. We present a uniform family with a membrane structure of depth d + 1 that
solves a problem complete for level d of the Polynomial Hierarchy
Profiles of dynamical systems and their algebra
The commutative semiring of finite, discrete-time dynamical
systems was introduced in order to study their (de)composition from an
algebraic point of view. However, many decision problems related to solving
polynomial equations over are intractable (or conjectured to be
so), and sometimes even undecidable. In order to take a more abstract look at
those problems, we introduce the notion of ``topographic'' profile of a
dynamical system with state transition function as
the sequence , where
is the number of states having distance , in terms of number of
applications of , from a limit cycle of . We prove that the set of
profiles is also a commutative semiring with respect to
operations compatible with those of (namely, disjoint union and
tensor product), and investigate its algebraic properties, such as its
irreducible elements and factorisations, as well as the computability and
complexity of solving polynomial equations over .Comment: 12 pages, 2 figure
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
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
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
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
Decomposition and factorisation of transients in Functional Graphs
Functional graphs (FGs) model the graph structures used to analyze the
behavior of functions from a discrete set to itself. In turn, such functions
are used to study real complex phenomena evolving in time. As the systems
involved can be quite large, it is interesting to decompose and factorize them
into several subgraphs acting together. Polynomial equations over functional
graphs provide a formal way to represent this decomposition and factorization
mechanism, and solving them validates or invalidates hypotheses on their
decomposability. The current solution method breaks down a single equation into
a series of \emph{basic} equations of the form (with , ,
and being FGs) to identify the possible solutions. However, it is able to
consider just FGs made of cycles only. This work proposes an algorithm for
solving these basic equations for general connected FGs. By exploiting a
connection with the cancellation problem, we prove that the upper bound to the
number of solutions is closely related to the size of the cycle in the
coefficient of the equation. The cancellation problem is also involved in
the main algorithms provided by the paper. We introduce a polynomial-time
semi-decision algorithm able to provide constraints that a potential solution
will have to satisfy if it exists. Then, exploiting the ideas introduced in the
first algorithm, we introduce a second exponential-time algorithm capable of
finding all solutions by integrating several `hacks' that try to keep the
exponential as tight as possible
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