Membrane systems with proteins embedded in membranes

Membrane computing is a biologically inspired computational paradigm. Motivated by brane calculi we investigate membrane systems which differ from conventional membrane systems by the following features: (1) biomolecules (proteins) can move through the regions of the systems, and can attach onto (and de-attach from) membranes, and (2) membranes can evolve depending on the attached molecules. The evolution of membranes is performed by using rules that are motivated by the operation of pinocytosis (the pino rule) and the operation of cellular dripping (the drip rule) that take place in living cells.We show that such membrane systems are computationally universal. We also show that if only the second feature is used then one can generate at least the family of Parikh images of the languages generated by programmed grammars without appearance checking (which contains non-semilinear sets of vectors).If, moreover, the use of pino/drip rules is non-cooperative (i.e., not dependent on the proteins attached to membranes), then one generates a family of sets of vectors that is strictly included in the family of semilinear sets of vectors.We also consider a number of decision problems concerning reachability of configurations and boundness. (C) 2008 Elsevier B.V. All rights reserved

Time-independent P systems

We introduce a class of P systems called timed P systems where to each rule is associated an integer that represents the time needed by the rule (reaction) to be entirely executed. The idea comes from cell biology where chemical reactions take certain times to be executed. In this work we are interested in a special class of P systems, called time-free, working always in the same way (i.e., always producing the same result) independently from the values associated to the execution time of their rules. Later we introduce a generalization of time-free P systems, namely clock-free P systems, where a time of execution is associated directly to each single application of the rules (in this case, different applications, even of the same rule, may take a different time to be executed). Several results are presented together with open problems and research proposals. © Springer-Verlag Berlin Heidelberg 2005

Time and synchronization in membrane systems

Membrane systems are parallel computational devices inspired from the cell functioning. Since the original definition, a standard feature of membrane systems is the fact that each rule of the system is executed in exactly one time-unit. However, this hypothesis seems not to have a counterpart in real world. In fact, in cells, chemical reactions might take different times to be exe-cuted. Therefore, a natural step is to associate to each rule of a membrane system a certain time of execution. We are interested in membrane systems, called time-free, working independently from the assigned execution time of the rules. A basic and interesting problem in time-free membrane systems consists in the synchronization of different rules, running in parallel, and having unknown execution times. Here, we present different ways to approach this problem within the framework of membrane systems. Several research proposals are also suggested

Computing using signals: From cells to P systems

In cell biology a fundamental topic is the study of how biological signals are managed by cells. Signals can arise from inside the cell or from the external environment and the correct answer to certain signals is essential for bacteria to survive in a certain environment. Starting from these biological motivations we consider a model of P systems where the computation is controlled by signals which move across the regions. In particular, we consider signals-based P systems where the symbol-objects cannot be moved and the evolution rules can be activated/ inactivated using a finite number of signals (signal-promoters) moved across the membranes; differently from standard P systems using promoters, in our case signal-promoters cannot be created during the computation. After discussing the biological motivations we show how this model becomes universal when it uses one catalyst and a bounded number of signal-promoters. Also results concerning signals-based P systems using non cooperative rules together with several open problems are presented. © Springer-Verlag 2005

Multiset random context grammars, checkers, and transducers

We introduce a general model of random context multiset grammars as well as the concept of multiset random context checkers and transducers. Our main results show how recursively enumerable sets of finite multisets can be generated using these models of computing; corresponding results for antiport P systems are established, too. © 2006 Elsevier Ltd. All rights reserved

Membrane Systems with Marked Membranes

Membrane computing is a biologically inspired computational paradigm. Motivated by brane calculi we investigate membrane systems which differ from conventional membrane systems by the following features: (1) biomolecules (proteins) can move through the regions of the systems, and can attach onto (and de-attach from) membranes, and (2) membranes can evolve depending on the attached molecules. The evolution of membranes is performed by using rules that are motivated by the operation of pinocytosis (the pino rule) and the operation of cellular dripping (the drip rule) that take place in living cells. We show that such membrane systems are computationally universal. We also show that if only the second feature is used then one can generate at least the family of Parikh images of the languages generated by programmed grammars without appearance checking (which contains non-semilinear sets of vectors). If, moreover, the use of pino/drip rules is non-cooperative (i.e., not dependent on the proteins attached to membranes), then one generates a family of sets of vectors that is strictly included in the family of semilinear sets of vectors. We also consider a number of decision problems concerning reachability of configurations and boundness. © 2007 Elsevier B.V. All rights reserved

Membrane systems with external control

We consider the idea of controlling the evolution of a membrane system. In particular, we investigate a model of membrane systems using promoted rules, where a string of promoters (called the control string) "travels" through the regions, activating the rules of the system. This control string is present in the skin region at the beginning of the computation - one can interpret that it has been inserted in the system before starting the computation - and it is "consumed", symbol by symbol, while traveling through the system. In this way, the inserted string drives the computation of the membrane system by controlling the activation of evolution rules. When the control string is entirely consumed and no rule can be applied anymore, then the system halts - this corresponds to a successful computation. The number of objects present in the output region is the result of such a computation. In this way, using a set of control strings (a control program), one generates a set of numbers. We also consider a more restrictive definition of a successful computation, and then study the corresponding model. In this paper we investigate the influence of the structure of control programs on the generative power. We demonstrate that different structures yield generative powers ranging from finite to recursively enumerable number sets. In determining the way that the control string moves through the regions, we consider two possible "strategies of traveling", and prove that they are similar as far as the generative power is concerned. © Springer-Verlag Berlin Heidelberg 2006