State Transition Dynamics

Classical dynamics concepts are analysed in the basic mathematical setting of state transition systems where time and space are both completely discrete and no structure is assumed on the state’s space. Interesting relationships between attractors and recurrence are identified and some features of chaos are expressed in simple, set theoretic terms. String dynamics is proposed as a unifying concept for dynamical systems arising from discrete models of computation, together with illustrative examples. The relevance of state transition systems and string dynamics is discussed from the perspective of molecular computing.

Formal Modelling of the Dynamic Behaviour of Biology-Inspired, Agent-Based Systems

Multi-agent systems are highly dynamic since the agents’ abilities and the system configuration often changes over time. In some ways, such multi-agent systems seem to behave like biological processes; new agents appear in the system, some others cease to exist, and communication between agents changes. One of the challenges is to attempt to formally model the dynamic configuration of multi-agent systems. Towards this aim, we present a formal method, namely X-machines, that can be used to formally specify, verify, and test individual agents. In addition, communicating X-machines provide a mechanism for allowing agents to communicate messages to each other. We utilize concepts from biological processes in order to identify and define a set of operations that are able to reconfigure a multi-agent system. In this chapter we present an example in which a biology-inspired system is incrementally built in order to meet our objective.

Computing Bacterial Evolvability Using Individual-Based Models

This chapter describes two approaches to individual-based modelling that are based on bacterial evolution and bacterial ecologies. Some history of the individual-based modelling approach is presented and contrasted to traditional methods. Two related models of bacterial evolution are then discussed in some detail. The first model consists of populations of bacterial cells, each bacterial cell containing a genome and many gene products derived from the genome. The genomes themselves are slowly mutated over time. As a result, this model contains multiple time scales and is very fine-grained. The second model employs a coarser-grained, agent-based architecture designed to explore the evolvability of adaptive behavioural strategies in artificial bacterial ecologies. The organisms in this approach are represented by mutating learning classifier systems. Finally, the subject of computability on parallel machines and clusters is applied to these models, with the aim of making them efficiently scalable to the point of being biologically realistic by containing sufficient numbers of complex individuals.

Membrane Computing

Membrane computing is a branch of natural computing whose initial goal was to abstract computing models from the structure and the functioning of living cells. The research was initiated about five years ago (at the end of 1998), and since that time the area has been developed significantly from a mathematical point of view. The basic types of results of this research concern the computability power (in comparison with the standard Turing machines and their restrictions) and the efficiency (the possibility to solve computationally hard problems, typically NP-complete problems, in a feasible time and typically polynomial). However, membrane computing has recently become attractive also as a framework for devising models of biological phenomena, with the tendency to provide tools for modelling the cell itself, not only the local processes. This chapter surveys the basic elements of membrane computing, somewhat in its “historical” evolution: from biology to computer science and mathematics and back to biology. The presentation is informal, without any technical detail, and an invitation to membrane computing intended to acquaint the nonmathematician reader with the main directions of research of the domain, the type of central results, and the possible lines of future development, including the possible interest of the biologist looking for discrete algorithmic tools for modelling cell phenomena.

Cellular Solutions to Some Numerical NP-Complete Problems

This chapter is devoted to the study of numerical NP-complete problems in the framework of cellular systems with membranes, also called P systems (Pun, 1998). The chapter presents efficient solutions to the subset sum and the knapsack problems. These solutions are obtained via families of P systems with the capability of generating an exponential working space in polynomial time. A simulation tool for P systems, written in Prolog, is also described. As an illustration of the use of this tool, the chapter includes a session in the Prolog simulator implementing an algorithm to solve one of the above problems.

Networks of Evolutionary Processors

The goal of this chapter is to survey, in a systematic and uniform way, the main results regarding different computational aspects of hybrid networks of evolutionary processors viewed both as generating and accepting devices, as well as solving problems with these mechanisms. We first show that generating hybrid networks of evolutionary processors are computationally complete. The same computational power is reached by accepting hybrid networks of evolutionary processors. Then, we define a computational complexity class of accepting these networks and prove that this class equals the traditional class NP. In another section, we present a few NP-complete problems and recall how they can be solved in linear time by accepting networks of evolutionary processors with linearly bounded resources (nodes, rules, symbols). Finally, we discuss some possible directions for further research.

On a Formal Model of the T Cell and Its Biological Feedback

In this chapter a model of the molecular networks, created by using a network of communicating automata, is described as a dynamic structure, discrete event system, and interesting theoretical results are provided. This formal model provides a detailed approach of the biological system, and its implementation is able to handle large amounts of data. This model is applied to T cell signalling networks. T cell shows a hierarchical organization depending on various factors. Some mechanisms are still unresolved, including contribution of each signalling pathway to each response type. The software tool produced is used to simulate and analyze the T cell behaviour. The simulation reflects, quite faithfully, the process of T cell activation and T cell responses. This increases the confidence in using this model and its implementation both as descriptive and prescriptive tools. The interactions that govern the T cell behaviour are simulated and analyzed, providing statistical correlations according to software experiments, together with new insights on signalling networks that trigger immunological responses. The software tool allows users to systematically perturb and monitor the components of a T cell molecular network, capturing biological information relevant to immunology.

Modeling Development Processes in MGS

Biology has long inspired unconventional models of computation to computer scientists. This chapter focuses on a model inspired by biological development both at the molecular and cellular levels. Such biological processes are particularly interesting for computer science because the dynamic organization emerges from many decentralized and local interactions that occur concurrently at several time and space scales. Thus, they provide a source of inspiration to solve various problems related to mobility, distributed systems, open systems, etc. The fundamental mechanisms of biological development are now understood as changes within a complex dynamical system. This chapter advocates that these fundamental mechanisms, although mainly developed in a continuous framework, can be rephrased in a discrete setting relying on the notion of rewriting in a topological setting. The discrete formulation is as formal as the continuous one, enables the simulation, and opens a way to the systematic study of the behavioral properties of the biological systems. Directly inspired from these developmental processes, the chapter presents an experimental programming language called MGS. MGS is dedicated to the modeling and simulation of dynamical systems with dynamical structures. The chapter illustrates the basic notions of MGS through several algorithmic examples and by sketching various biological models.

DNA Computing and Errors

This chapter looks at the question of managing errors that arise in DNA-based computation. Due to the inaccuracy of biochemical reactions, the experimental implementation of a DNA computation may lead to incorrectly calculated results. This chapter explores different methods that can assist in the reduction of such occurrences. The solutions to the problem of erroneous biocomputations are presented from the perspective of computer science techniques. Three main aspects of dealing with errors are covered: software simulations, algorithmic approaches, and theoretical methods. The objective of this survey is to explain how these tools can reduce errors associated with DNA computing.