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We study a modelling framework and computational paradigm called Colonies of Synchronizing Agents (CSAs), which abstracts intracellular and intercellular mechanisms of biological tissues. The model is based on a multiset of agents (cells) in a common environment (a tissue). Each agent has a local contents, stored in the form of a multiset of atomic objects (e.g., representing molecules), updated by multiset rewriting rules which may act on individual agents (intracellular action) or synchronize the contents of pairs of agents (intercellular action).

In this paper we investigate dynamic properties of CSAs, by means of temporal logic, and we give a logical characterization of some notions inspired by biology such as robustness, mutants and species. We reveal the relation that exists between the concept of robustness for CSAs and the bisimulation relation on colonies. We also present some decidability results for particular cases of robustness.

Reaction systems are a functional model of interactions between biochemical reactions. They define functions on finite sets (over a common finite domain). In this paper, we investigate combinatorial properties of functions defined by reaction systems. In particular, we provide analytical approximations of combinatorial properties of random reaction systems, with a focus on the probability of whether a system lives or dies. Based on these results, we can create parameterized random reaction systems that rarely die. We also empirically analyze the length of time before such a system enters cyclic behavior, and find that the time is related to the behavior of completely random functions on a smaller domain.

Reaction systems are a formal model of interactions between biochemical reactions. They consist of sets of reactions, where each reaction is classified by its set of reactants (needed for the reaction to take place), its set of inhibitors (each of which prevents the reaction from taking place), and its set of products (produced when the reaction takes place) – the set of reactants and inhibitors form the resources of the reaction. Each reaction system defines a (transition) function on its set of states. (States here are subsets of an a priori given set of biochemical entities.) In this paper we investigate properties of functions defined by reaction systems. In particular, we investigate how the power of defining functions depends on available resources, and we demonstrate that with small resources one can define functions exhibiting complex behavior.

Reaction systems are a formal framework for investigating processes carried out by biochemical reactions. This paper is an introduction to reaction systems. It provides basic notions together with the underlying intuition and motivation as well as two examples (a binary counter and transition systems) of "programming" with reaction systems. It also provides a tour of some research themes.

Reaction systems are an abstract model of biochemical reactions in the living cell within a framework of finite (though often large) discrete dynamical systems. In this setting, this paper provides an analytical and experimental study of stability. The notion of stability is defined in terms of the way in which small perturbations to the initial state of a system are likely to change the system's eventual behavior. At the stable end of the spectrum, there is likely to be no change; but at the unstable end, small perturbations take the system into a state that is probabilistically the same as a randomly selected state, similar to chaotic behavior in continuous dynamical systems.

This paper discusses research frontiers of membrane computing by presenting current open problems and research topics, together with the relevant background and motivation.

Reaction systems are a model of computation inspired by biochemical reactions involving reactants, inhibitors and products from a finite background set. We define a notion of multi-step simulation among reaction systems and derive a classification with respect to the amount of resources (reactants and inhibitors) involved in each reaction. We prove that “simple” reaction systems, having at most one reactant and one inhibitor per reaction, suffice in order to simulate arbitrary systems. Finally, we show that the equivalence relation of mutual simulation induces exactly five linearly ordered classes of reaction systems characterizing well-known subclasses of the functions over Boolean lattices, such as the constant, additive (join-semilattice endomorphisms), monotone, and antitone functions.

Some mathematical aspects of reaction systems introduced by Ehrenfeucht and Rozenberg are considered. Ehrenfeucht et al. have previously obtained a complete classification of functions specified by minimal reaction systems in terms of certain closure properties of the specified functions. In this work, a refined proof of this classification with slight extension is obtained. Furthemore, the recently introduced notion of reaction system rank is studied for functions belonging to this class, as well as for focus functions, the latter which play a significant role in the proof of the classification theorem.

This paper studies mathematical properties of reaction systems that were introduced by Ehrenfeucht and Rozenberg as computational models inspired by biochemical reaction in the living cells. In particular, we continue the study on the generative power of functions specified by minimal reaction systems under composition initiated by Salomaa. Allowing degenerate reaction systems, functions specified by minimal reaction systems over a quarternary alphabet that are permutations generate the alternating group on the power set of the background set.

Virus machines are computational devices inspired by the movement of viruses between hosts and their capacity to replicate using the resources of the hosts. This behavior is controlled by an external graph of instructions that opens different channels of the system to make viruses capable of moving. This model of computation has been demonstrated to be as powerful as turing machines by different methods: by generating Diophantine sets, by computing partial recursive functions and by simulating register machines. It is interesting to investigate the practical use cases of this model in terms of possibilities and efficiency. In this work, we give the basic modules to create an arithmetic calculator. As a practical application, two pairing functions are calculated by means of two different virus machines. Pairing functions are important resources in the field of cryptography. The functions calculated are the Cantor pairing function and the Gödel pairing function.

In this paper, two natural production inventory models based on fuzzy total production inventory cost with the preference of a decision maker are introduced, and combined by natural number parameters in which values are linguistic values in natural language, crisp real number variables, and fuzzy number variables. These are the one natural production inventory model for crisp production quantity, and the other natural production inventory model for fuzzy production quantity. The natural arithmetical operations of both natural numbers and fuzzy numbers by Function Principle are used to compute fuzzy total production inventory cost of each natural production inventory model. Graded k-preference integration representation method is discussed for defuzzifying fuzzy total production inventory cost by preference of decision maker. Furthermore, Extension of the Lagrangean method is used to solve inequality constrain problem in our natural production inventory model. We find out that our optimal solutions can be specified to the classical production inventory model when preference 0.5 of decision maker and natural numbers and fuzzy numbers in our models are crisp real numbers.

In this paper we present in a tutorial fashion the framework of reaction systems — a formal approach to investigating processes instigated by the living cell. The main idea behind this approach is that this functioning is determined by interactions between biochemical reactions, and these interactions are based on two mechanisms, facilitation and inhibition.

Role of f-granulation in handling uncertainty in machine intelligence and its significance as a facet of natural computation are discussed. Its modeling through judicious integration of rough and fuzzy sets is explained. Several tasks like case generation, clustering, classification and segmentation are described in rough-fuzzy framework demonstrating the role of f-granulation and the resulting merits. A definition of generalized rough sets is given considering both the set and granules as crisp and/or fuzzy. Based on that new entropy measures are defined using exponential and logarithmic gain functions. The superiority of rough-fuzzy integration, in terms of performance and computation time, is illustrated for the tasks of case mining in large data sets, segmenting brain MR images, and classifying remotely sensed images as examples. Neighbourhood rough sets are capable of better dimensionality reduction. The effect of fuzzy-granules and generalizations in rough sets is demonstrated for image segmentation. The article includes some of the results published elsewhere.