Modeling and Analysis of Firewalls by (Tissue-like) P Systems

We propose to use tissue-like P systems as a tool to model and analyse the security properties of ¯rewall systems. The idea comes from a clear analogy between firewall rules and P systems rules: they both modify and or move objects (data packets, or symbols of an alphabet) among the regions of the system. The use of P systems for modeling packet filters, routers and firewalls gives the possibility to check - and possibly mathematically prove - some security properties

Formal Modelling and Simulation of Biological Systems with Spatiality

In Systems Biology, spatial modelling allows an accurate description of phenomena whose behaviour is influenced by the spatial arrangement of the elements. In this thesis, we present various modelling formalisms with spatial features, each using a different abstraction level of the real space. From the formalisms with the most abstract notion of space, to the most concrete, we formally define the MIM Calculus with compartments, the Spatial P systems, and the Spatial CLS. Each formalism is suitable for the description of different kinds of systems, which call for the use of different space modelling abstractions. We present models of various real-world systems which benefit from the ability to precisely describe space-dependent behaviours. We define the MIM Calculus, inspired by Molecular Interaction Maps, a graphical notation for bioregulatory networks. The MIM Calculus provides high-level operators with a direct biological meaning, which are used to describe the interaction capabilities of the elements of such systems. Its spatial extension includes the most abstract notion of space, namely it only allows the modelling of compartments. Such a feature allows distinguishing only the abstract position where an element is, identified by the name of the compartment. Subsequently, we propose a spatial extension to the membrane computing formalism P systems. In this case, we follow a more precise approach to spatial modelling, by embedding membranes and objects in a two-dimensional discrete space. Some objects of a Spatial P system can be declared as mutually exclusive objects, with the constraint that each position can accommodate at most one of them. The distinction between ordinary and mutually exclusive objects can be thought of as an abstraction on the size of the objects. We study the computational complexity of the formalism and the problem of efficient simulation of some kinds of models. Finally, we present the Spatial Calculus of Looping Sequences (Spatial CLS), which is an extension of the Calculus of Looping Sequences (CLS), a formalism geared towards the modelling of cellular systems. In this case, models are based on two/three dimensional continuous space, and allow an accurate description of the motion of the elements, and of their size. In particular, Spatial CLS allows the description of the space occupied by elements and membranes, which can change their sizes dynamically as the system evolves. Space conflicts which may occur can be resolved by performing a rearrangement of elements and membranes. As example applications of the calculus we present a model of cell proliferation, and a model of the quorum sensing process in Pseudomonas aeruginosa

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