288 research outputs found
Minimization Strategies for Maximally Parallel Multiset Rewriting Systems
Maximally parallel multiset rewriting systems (MPMRS) give a convenient way
to express relations between unstructured objects. The functioning of various
computational devices may be expressed in terms of MPMRS (e.g., register
machines and many variants of P systems). In particular, this means that MPMRS
are computationally complete; however, a direct translation leads to quite a
big number of rules. Like for other classes of computationally complete
devices, there is a challenge to find a universal system having the smallest
number of rules. In this article we present different rule minimization
strategies for MPMRS based on encodings and structural transformations. We
apply these strategies to the translation of a small universal register machine
(Korec, 1996) and we show that there exists a universal MPMRS with 23 rules.
Since MPMRS are identical to a restricted variant of P systems with antiport
rules, the results we obtained improve previously known results on the number
of rules for those systems.Comment: This article is an improved version of [1
Introducing the Concept of Activation and Blocking of Rules in the General Framework for Regulated Rewriting in Sequential Grammars
We introduce new possibilities to control the application of rules based on
the preceding application of rules which can be de ned for a general model of sequential
grammars and we show some similarities to other control mechanisms as graph-controlled
grammars and matrix grammars with and without applicability checking as well as gram-
mars with random context conditions and ordered grammars. Using both activation and
blocking of rules, in the string and in the multiset case we can show computational com-
pleteness of context-free grammars equipped with the control mechanism of activation
and blocking of rules even when using only two nonterminal symbols
One-Membrane P Systems with Activation and Blocking of Rules
We introduce new possibilities to control the application of rules based on
the preceding applications, which can be de ned in a general way for (hierarchical) P
systems and the main known derivation modes. Computational completeness can be
obtained even for one-membrane P systems with non-cooperative rules and using both
activation and blocking of rules, especially for the set modes of derivation.
When we allow the application of rules to in
uence the application of rules in previous
derivation steps, applying a non-conservative semantics for what we consider to be a
derivation step, we can even \go beyond Turing"
Maximally Parallel Multiset-Rewriting Systems: Browsing the Configurations
The aim of this research is to produce an algorithm for the software that
would let a researcher to observe the evolution of maximally parallel multiset-rewriting
systems with permitting and forbidding contexts, browsing the configuration space by
following transitions like following hyperlinks in the World-Wide Web.
The relationships of maximally parallel multiset-rewriting systems with other rewriting systems are investigated, such as Petri nets, different kinds of P systems, Lindenmayer
systems, grammar systems, regulated grammars
On the Power of Deterministic EC P Systems
It is commonly believed that a signi¯cant part of the computational
power of membrane systems comes from their inherent non-determinism. Re-
cently, R. Freund and Gh. P¸aun have considered deterministic P systems, and
formulated the general question whether the computing (generative) capacity
of non-deterministic P systems is strictly larger than the (recognizing) capacity
of their deterministic counterpart.
In this paper, we study the computational power of deterministic P systems
in the evolution{communication framework. It is known that, in the genera-
tive case, two membranes are enough for universality. For the deterministic
systems, we obtain the universality with three membranes, leaving the original
problem open
(Tissue) P Systems with Vesicles of Multisets
We consider tissue P systems working on vesicles of multisets with the very
simple operations of insertion, deletion, and substitution of single objects.
With the whole multiset being enclosed in a vesicle, sending it to a target
cell can be indicated in those simple rules working on the multiset. As
derivation modes we consider the sequential mode, where exactly one rule is
applied in a derivation step, and the set maximal mode, where in each
derivation step a non-extendable set of rules is applied. With the set maximal
mode, computational completeness can already be obtained with tissue P systems
having a tree structure, whereas tissue P systems even with an arbitrary
communication structure are not computationally complete when working in the
sequential mode. Adding polarizations (-1, 0, 1 are sufficient) allows for
obtaining computational completeness even for tissue P systems working in the
sequential mode.Comment: In Proceedings AFL 2017, arXiv:1708.0622
Communication in membrana Systems with symbol Objects.
Esta tesis está dedicada a los sistemas de membranas con objetos-símbolo como marco teórico de los sistemas paralelos y distribuidos de procesamiento de multiconjuntos.Una computación de parada puede aceptar, generar o procesar un número, un vector o una palabra; por tanto el sistema define globalmente (a través de los resultados de todas sus computaciones) un conjunto de números, de vectores, de palabras (es decir, un lenguaje), o bien una función. En esta tesis estudiamos la capacidad de estos sistemas para resolver problemas particulares, así como su potencia computacional. Por ejemplo, las familias de lenguajes definidas por diversas clases de estos sistemas se comparan con las familias clásicas, esto es, lenguajes regulares, independientes del contexto, generados por sistemas 0L tabulados extendidos, generados por gramáticas matriciales sin chequeo de apariciones, recursivamente enumerables, etc. Se prestará especial atención a la comunicación de objetos entre regiones y a las distintas formas de cooperación entre ellos.Se pretende (Sección 3.4) realizar una formalización los sistemas de membranas y construir una herramienta tipo software para la variante que usa cooperación no distribuida, el navegador de configuraciones, es decir, un simulador, en el cual el usuario selecciona la siguiente configuración entre todas las posibles, estando permitido volver hacia atrás. Se considerarán diversos modelos distribuidos. En el modelo de evolución y comunicación (Capítulo 4) separamos las reglas tipo-reescritura y las reglas de transporte (llamadas symport y antiport). Los sistemas de bombeo de protones (proton pumping, Secciones 4.8, 4.9) constituyen una variante de los sistemas de evolución y comunicación con un modo restrictivo de cooperación. Un modelo especial de computación con membranas es el modelo puramente comunicativo, en el cual los objetos traspasan juntos una membrana. Estudiamos la potencia computacional de las sistemas de membranas con symport/antiport de 2 o 3 objetos (Capítulo 5) y la potencia computacional de las sistemas de membranas con alfabeto limitado (Capítulo 6).El determinismo (Secciones 4.7, 5.5, etc.) es una característica especial (restrictiva) de los sistemas computacionales. Se pondrá especial énfasis en analizar si esta restricción reduce o no la potencia computacional de los mismos. Los resultados obtenidos para sistemas de bombeo del protones están transferidos (Sección 7.3) a sistemas con catalizadores bistabiles. Unos ejemplos de aplicación concreta de los sistemas de membranas (Secciones 7.1, 7.2) son la resolución de problemas NP-completos en tiempo polinomial y la resolución de problemas de ordenación.This thesis deals with membrane systems with symbol objects as a theoretical framework of distributed parallel multiset processing systems.A halting computation can accept, generate or process a number, a vector or a word, so the system globally defines (by the results of all its computations) a set of numbers or a set of vectors or a set of words, (i.e., a language), or a function. The ability of these systems to solve particular problems is investigated, as well as their computational power, e.g., the language families defined by different classes of these systems are compared to the classical ones, i.e., regular, context-free, languages generated by extended tabled 0L systems, languages generated by matrix grammars without appearance checking, recursively enumerable languages, etc. Special attention is paid to communication of objects between the regions and to the ways of cooperation between the objects.An attempt to formalize the membrane systems is made (Section 3.4), and a software tool is constructed for the non-distributed cooperative variant, the configuration browser, i.e., a simulator, where the user chooses the next configuration among the possible ones and can go back. Different distributed models are considered. In the evolution-communication model (Chapter 4) rewriting-like rules are separated from transport rules. Proton pumping systems (Sections 4.8, 4.9) are a variant of the evolution-communication systems with a restricted way of cooperation. A special membrane computing model is a purely communicative one: the objects are moved together through a membrane. We study the computational power of membrane systems with symport/antiport of 2 or 3 objects (Chapter 5) and the computational power of membrane systems with a limited alphabet (Chapter 6).Determinism (Sections 4.7, 5.5, etc.) is a special property of computational systems; the question of whether this restriction reduces the computational power is addressed. The results on proton pumping systems can be carried over (Section 7.3) to the systems with bi-stable catalysts. Some particular examples of membrane systems applications are solving NP-complete problems in polynomial time, and solving the sorting problem
A Note on P Systems with Activators
The usual assumption in P systems behavior is that of maximal
parallelism, however in living cells it is not the case because they have a limited
number of enzymes. The aim of this paper is to try to merge these ideas by
introducing a notion of activator - a formal model of enzyme as a usual symbol-
object, more or less a middle notion between a catalyst and a promoter. Each
activator executes one (context-free) rule, and can evolve in the same step.
The rules will need activators to be applied, so the parallelism of each rule is
maximal, but limited to the number of its activators.
Such systems can generate any recursively enumerable language or determinis-
tically accept any recursively enumerable set of vectors of nonnegative integers.
It is open what is the power of P systems with uniport rules and activator
Deterministic Non-cooperative P Systems with Strong Context Conditions
We continue the line of research of deterministic parallel non-cooperative
multiset rewriting with control. We here generalize control, i.e., rule applicability context
conditions, from promoters and inhibitors checking presence or absence of certain object
up to some bound, to regular and even stronger predicates, focusing at predicates over
multiplicity of one symbol at a time
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
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