The P systems were recently introduced as distributed parallel computing models of a biochemical type. Multisets of objects are placed in a hierarchical structure of membranes and they evolve according to given rules, which are applied in a synchronous manner: at each step, all objects which can evolve, from all membranes, must evolve. We consider here the case when this restriction is removed. As expected, unsynchronized systems (even using catalysts) are weaker than the synchronized ones, providing that no priority relation among rules is considered. The power of P systems is not diminished when a priority is used and, moreover, the catalysts can change their states, among two possible states for each catalyst.
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With inspiration from the economic reality, where numbers are basic entities to work with, we propose a genuinely new kind of P systems, where numerical variables evolve, starting from initial values, by means of production functions and repartition protocols. We prove that non-deterministic systems of this type, using polynomial production functions, characterize the Turing computable sets of natural numbers, while deterministic systems, with polynomial production functions having non-negative coefficients, compute strictly more than semilinear sets of natural numbers. A series of research topics to be addressed in this framework are mentioned.
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In this paper we discuss some relationships between grammar systems and P systems (membrane systems), two areas of computer science dealing with distributed computing models, but with different motivations and different types of basic ingredients. We extend one of the most important communication protocols of cooperating distributed (CD) grammar systems, the so-called t-derivation mode, to P systems with string-objects: if no rule can be applied to a string in a region of a P system, then the string is moved to a neighbouring region, depending on the communication mode either in exactly one direction (in or out) or in both directions. We describe the computational power of the obtained classes of P systems in comparison with families of languages generated by grammars in the Chomsky hierarchy or with CD grammar systems and formulate several problems for future research.
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Inspired from biochemistry and DNA computing, we introduce several variants of controlled concatenation of strings and languages: a finite set of pairs of strings is given and two arbitrary strings are concatenated only when among their substrings (scattered substrings, of various forms) we can find a pair in this control set. Five types of non-iterated and iterated (like Kleene closure) conditional concatenations are considered. The closure properties of abstract families of languages (hence also of families in the Chomsky hierarchy) are settled. They are similar to the closure properties under usual concatenation and Kleene closure. A representation of regular languages in terms of these operations (and a coding) is also given. Then, we use the new concatenation operations as basic operations in Chomsky grammars: rewriting a nonterminal means concatenating a new string with the strings to the left and the right of that nonterminal, hence restricted concatenations can be used. Context-free grammars working in this restricted manner can generate non-context-free languages; in one case, characterizations of recursively enumerable or of context-sensitive languages are obtained, depending on using or not erasing rules. Some topics for further research are also suggested.
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A membrane computing system (also called P system) consists of computing cells which are organized hierarchically by the inclusion relation: cells may include cells, which again may include cells, etc. Each cell is enclosed by its membrane. Each cell is an independent computing agent with its own computing program, which produces objects. The interaction between cells consists of the exchange of objects through membranes. The output of a computation is a partially ordered set of objects which leave the system through its external membrane. The fundamental properties of computations in such P systems with external output are investigated. These include the computing power, normal forms, and basic decision problems.
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This paper continues research on membrane systems which function by communication only, meaning that there are no evolving rules for molecules. The whole computation process relies on passage of molecules through membranes - this provides communication between regions of the membrane system. Next to transport of single molecules through membranes (uniport) we also study a coupled transport of molecules, with two molecules passing either in the same direction (symport) or in opposite directions (antiport). We study the computational power of such membrane systems and prove that using only symport one gets Turing universality. Moreover, we prove that five membranes suffice to get Turing universality, and the number of membranes can be decreased to three if forbidding context conditions for transport are used.
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We bring together two topics recently introduced in membrane computing, the much investigated spiking neural P systems (in short, SN P systems), inspired from the way the neurons communicate through spikes, and the dP systems (distributed P systems, with components which “read” strings from the environment and then cooperate in accepting their concatenation). The goal is to introduce SN dP systems, and to this aim we first introduce SN P systems with the possibility to input, at their request, spikes from the environment; this is done by so-called request rules. A preliminary investigation of the obtained SN dP systems (they can also be called automata) is carried out. As expected, request rules are useful, while the distribution in terms of dP systems can handle languages which cannot be generated by usual SN P systems. We always work with extended SN P systems; the non-extended case, as well as several other natural questions remain open.
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This paper proposes a way to incorporate the idea of spiking neurons into the area of membrane computing, and to this aim we introduce a class of neural-like P systems which we call spiking neural P systems (in short, SN P systems). In these devices, the time (when the neurons fire and/or spike) plays an essential role. For instance, the result of a computation is the time between the moments when a specified neuron spikes. Seen as number computing devices, SN P systems are shown to be computationally complete (both in the generating and accepting modes, in the latter case also when restricting to deterministic systems). If the number of spikes present in the system is bounded, then the power of SN P systems falls drastically, and we get a characterization of semilinear sets. A series of research topics and open problems are formulated.
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We consider two complexity parameters related to the graph of reachable configurations of a given P system, namely the outdegree as a measure of the degree of non-determinism, and the indegree as a measure of the degree of confluence. These parameters can be defined for both the generative and the accepting mode of using a P system. We investigate here these parameters in what concerns hierarchies and decidability issues. We prove that all hierarchies have only two levels and that all considered decidability problems have a negative answer.
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We continue the study of spiking neural P systems by considering these computing devices as binary string generators: the set of spike trains of halting computations of a given system constitutes the language generated by that system. Although the "direct" generative capacity of spiking neural P systems is rather restricted (some very simple languages cannot be generated in this framework), regular languages are inverse-morphic images of languages of finite spiking neural P systems, and recursively enumerable languages are projections of inverse-morphic images of languages generated by spiking neural P systems.
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This paper proposes and investigates the possibility of transforming a configuration of a P system (the membrane structure and the multisets of symbol-objects present in the compartments) into another configuration by means of a given set of rules to be applied to the membranes and to the multisets of objects. Although this transformation is obtained during the computation in a P system, we consider it as a goal per se, as a pre-computation phase, when the system itself is built. In this framework, several important problems appear: the edit-distance between configurations (with respect to a given set of editing rules), normal forms, the reachability of configurations, or the existence of single configurations from which a given family of configurations can be constructed, only to mention a few. We investigate here some of these questions; the paper is mainly devoted to formulating problems in the new framework, to calling attention to the possible extensions and the usefulness of the present approach.
The feasibility of using laccase from Trametes versicolor for degradation of aromatic hydrocar-bons has been investigated. In the experiments, benzo[a]pyrene (BaP) was used. Laccase was immobilized onto mesoporous micelle-templated silica such as Santa Barbara Amorphous (SBA-15) and hexagonal mesoporous silica (HMS) as well as corresponding amino-functionalized supports. The best results were obtained for SBA-15 mesoporous silica however the HMS support could be as well considered for this type of application. The reusability of laccase immobilized into both silica supports was tested for five reaction cycles and the conversion reached about 70% of the initial value.
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