Formal Verification of P Systems

Membrane systems, also known as P systems, constitute an innovative computational paradigm inspired by the structure and dynamics of the living cell. A P system consists of a hierarchical arrangement of compartments and a finite set of multiset rewriting and communication rules, which operate in a maximally parallel manner. The organic vision of concurrent dynamics captured by membrane systems stands in antithesis with conventional formal modelling methods which focus on algebraic descriptions of distributed systems. As a consequence, verifying such models in a mathematically rigorous way is often elusive and indeed counter-intuitive when considering established approaches, which generally require sequential process representations or highly abstract theoretical frameworks. The prevalent investigations with this objective in the field of membrane computing are ambivalent and inconclusive in the wider application scope of P systems. In this thesis we directly address the formal verification of membrane systems by means of model checking. A fundamental distinction between the agnostic perspective on parallelism, advocated by process calculi, and P systems' emblematic maximally parallel execution strategy is identified. On this basis, we establish that an intuitional translation to traditional process models is inadequate for the purpose of formal verification, due to a state space growth disparity. The observation is essential for this research project: on one hand it implies the feasibility of model checking P systems, and on the other hand it underlines the suitability of this formal verification technique in the context of membrane computing. Model checking entails an exhaustive state space exploration and does not derive inferences based on the independent instructions comprising a state transition. In this respect, we define a new sequential modelling strategy which is optimal for membrane systems and targets the SPIN formal verification tool. We introduce elementary P systems, a distributed computational model which subsumes the feature diversity of the membrane computing paradigm and distils its functional vocabulary. A suite of supporting software tools which gravitate around this formalism has also been developed, comprising of 1. the eps modelling language for elementary P systems; 2. a parser for the eps specification; 3. a model simulator and 4. a translation tool which targets the Promela specification of the SPIN model checker. The formal verification approach proposed in this thesis is progressively demonstrated in four heterogeneous case studies, featuring 1. a parallel algorithm applicable to a structured model; 2. a linear time solution to an NP-complete problem; 3. an innovative implementation of the Dining Philosophers scenario (a synchronisation problem) using an elementary P system and 4. a quantitative analysis of a simple random process implemented without the support of a probabilistic model

Using A Kernel P System to Solve The 3-Col Problem

The newly introduced Kernel P systems offer an unitary and elegant way of integrating established features of existing P system variants with new elements with potential value for formal modelling. This paper presents a case study illustrating the expressive power and efficiency of kernel P systems on the 3-Col problem. The use of model checking (in particular of Spin) for formal verification of kernel P systems is also discussed and illustrated in this case.Ministerio de Ciencia e Innovación TIN2009–13192Junta de Andalucía P08–TIC–0420

Kernel P Systems - Version 1

A basic P system, called kernel P system4 (kP system for short), combining features of di erent P systems introduced and studied so far is de ned and discussed. The structure of such systems is de ned as a dynamic graph, similar to tissue-like P systems, the objects are organised as multisets, and the rules in each compartment, rewriting and communication together with system structure changing rules, are applied in accordance with a speci c execution strategy. The de nition of kP systems is introduced and some examples illustrate this concept. Two classes of P systems, namely neural-like and generalised communicating P systems are simulated by kP systems. Some case studies prove the expressive power of these systems.Ministerio de Economía y Competitividad TIN2012-37434Junta de Andalucía P08-TIC-0420

Towards an Integrated Approach for Model Simulation, Property Extraction and Veri cation of P Systems

This paper presents an integrated approach for model simulation, property extraction and formal veri cation of P systems, illustrated on a tissue P system with active membranes solving the 3-colouring problem. The paper focuses on this problem and reports the invariants and the properties extracted and veri ed using a series of tools (Daikon, MeCoSim, Maple, Spin, ProB) and languages (P{Lingua, Promela, Event-B). Appropriate tools and integration plugins, which facilitate and even automate the steps involved in the aforementioned approach, have also been developed. The case study chosen is complex (it involves an exponential growth of the number of states through the use of membrane division rules) and the properties obtained are non-trivial.Ministerio de Ciencia e Innovación TIN2009–13192Junta de Andalucía P08–TIC–0420

Admissibility and Non-Uniform Dichotomy for Differential Systems

The problem of nonuniform exponential dichotomy of linear differential systems in Banach spaces is discussed. It is established a connection between the admissibility of a pair of certain function spaces which are translations invariant, on one hand, and the nonuniform exponential dichotomy of differential systems, on the other. Also, Some results due to Hartman, Massera, Schäffer and Coppel are generalized as well

Some Landau Type Inequalities for Functions whose Derivates are Hölder Continuous

Some inequalities of Landau type for functions whose derivates satisfy Hölder’s condition are pointed out

Granular sloshing absorbers for vibration control

Tall, flexible structures may be exposed to excessive oscillations when subjected to wind, earthquakes or other shocks. Passive and active absorbers are employed, often at great expense, to stabilise the structures for the safety and comfort of the occupants. Current passive damper technologies include Tuned Mass Dampers and Tuned Liquid Dampers. These devices provide optimal damping at the natural frequency of the structure. This thesis proposes a novel passive damping device, that uses a granular material sloshing in a rotating cylindrical container as the energy sink. Tuning of a granular sloshing absorber is shown to be effective using a laboratory prototype, increasing the inherent damping of the structure by two orders of magnitude with an added mass of about 1%. The energy dissipation is found to be dependent on granular material properties and speed of rotation. A numerical model is also developed and validated, and can be used as a design tool for a large scale absorber. In this thesis a new and innovative passive damper design is proved on a small prototype and numerical tools required to implement a real device are developed. These tools can be used to create safer infrastructure or more comfortable buildings

A Kernel P System

Abstract. A basic P system, called kernel P system (kP system for short), covering features of different P systems introduced and studied so far is defined and discussed. It is a relatively low level specification system aiming to cover features exhibited by most of the problems modelled so far using P system formalisms. A small set of rules and specific strategies to run the system step by step are presented. Some preliminary results regarding the relationships between kP systems and other classes of P systems, like neural-like P systems and P systems with active membranes, are presented. Examples illustrating the behaviour of kP systems or showing how a sorting algorithm is modelled with various classes of P systems are provided. Further developments of this class of P systems are finally briefly discussed.

Some Classes of Generalised Communicating P Systems and Simple Kernel P Systems

Abstract. In this paper, four restricted variants of the generalised communicating P systems are considered and their computational power is investigated. In all these cases better results are produced, with respect to the number of cells involved, than those provided so far in the literature. Connections between the variants considered and recently introduced kernel P systems are investigated