Non-confluence in divisionless P systems with active membranes

We describe a solution to the SAT problem via non-confluent P systems with active membranes, without using membrane division rules. Furthermore, we provide an algorithm for simulating such devices on a nondeterministic Turing machine with a polynomial slowdown. Together, these results prove that the complexity class of problems solvable non-confluently and in polynomial time by this kind of P system is exactly the class .     

Languages generated by P systems with active membranes

We propose an alternative approach to generate languages by means of P systems: building up an appropriate representation for a string by means of a corresponding membrane structure and then generating the string by visiting the membrane structure according to a well-specified strategy. To this aim, we consider P systems with active membranes, allowing membrane creation or division or duplication and dissolution, where the output of a computation may be obtained either by visiting the tree associated with the membrane structure, or by following the traces of a specific object, called traveller, or sending out the objects. For each of these approaches, we provide characterizations of recursively enumerable languages based on P systems that use different sets of operations for modifying the membrane structure. Francesco Bernardini: He started his Ph.D. at the University of Sheffield in December 2002 after having previously got a master degree in Computer Science from the University of Pisa in Italy. His research is dedicated to the study of theoretical aspects of membrane computing (P systems) and discrete models of biological systems based on P systems. Marian Gheorghe, Ph.D.: His main research interests are in computational models and their applications to software modelling and testing, formal specifications of agent based systems, software engineering. He was investigating computational power of various generative devices (regular, context-free, fully initial; grammar systems; L-systems and variants). He is currently interested in natural computing (membrane calculus) and biological modelling.     

A Prolog simulator for deterministic P systems with active membranes

In this paper we propose a new way to represent P systems with active membranes based on Logic Programming techniques. This representation allows us to express the set of rules and the configuration of the P system in each step of the evolution as literals of an appropriate language of first order logic. We provide a Prolog program to simulate, the evolution of these P systems and present some auxiliary tools to simulate the evolution of a P system with active membranes using 2-division which solves the SAT problem following the techniques presented in Reference.¹⁰ Andrés Cordón-Franco: He is a member of the Department of Computer Science and Artificial Intelligence at the University of Sevilla (Spain). He is also a member of the research group on Natural Computing of the University of Seville. His research interest includes Mathematical Logic, Logic in Computer Science, and Membrane Computing, both from a theoretical and from a practical (software implementation) point of view. Miguel A. Gutiérrez-Naranjo: He is an assistant professor in the Computer Science and Artificial Intelligence Department at University of Sevilla, Spain. He is also a member of the Research Group on Natural Computing of the University of Seville. His research interest includes Machine Learning, Logic Programming and Membrane Computing, both from a theoretical and a practical point of view. Mario J. Pérez-Jiménez, Ph.D.: He is professor of Department of Computer Science and Artificial Intelligence at University of Seville, where he is the head of the Group of Research on Natural Computing, He has published 8 books of Mathematics and Computation, and more than 90 scientific articles in prestigious scientific journals. He is member of European Molecular Computing Consortium. Fernando Sancho-Caparrini: He is a member of the Department of Computer Science and Artificial Intelligence at the University of Sevilla (Spain). He is also a member of the research group on Natural Computing of the University of Seville. His research interest includes Complex Systems, DNA Computing, Logic in Computer Science, and Membrane Computing, both from a theoretical and from a practical point of view.     

P systems with active membranes and without polarizations

P systems with active membranes but without using electrical charges (polarizations) are shown to be complete for generating recursively enumerable string languages when working on string objects and using only rules with membrane transitions as well as rules with membrane dissolving and elementary membrane division, but also when using various other kinds of rules, even including a new type of rules allowing for membrane generation. In particular, allowing for changing membrane labels turns out to be a very powerful control feature.     

Solving multidimensional 0–1 knapsack problem by P systems with input and active membranes

Membrane systems are biologically motivated theoretical models of distributed and parallel computing. In this paper, we present a membrane algorithm to solve multidimensional 0–1 knapsack problem in linear time by recognizer P systems with input and with active membranes using 2-division. This algorithm can also be modified to solve general 0–1 integer programming problem.     

An efficient time-free solution to SAT problem by P systems with proteins on membranes

P systems with proteins on membranes are a class of bio-inspired computing models, where the execution of each rule completes in exactly one time unit. However, in living cells, the execution time of biochemical reactions is difficult to know precisely because of various uncontrollable factors. In this work, we present a time-free uniform solution to SAT problem by P systems with proteins on membranes in the sense that the correctness of the solution is irrelevant to the times associated with the involved rules, and the P systems are constructed from the sizes of instances.     

P systems with local graph productions

P systems (membrane systems) of various types so far mainly have been considered as computing devices working on multisets or strings. In this paper we investigate P systems with local graph productions generating weakly connected directed graphs. At least when equipped with a priority relation on the rules, such P systems can generate any recursively enumerable language of weakly connected directed graphs with only one membrane. Rudolf Freund, Ph.D.: He holds a master and doctor degree in computer science and a master degree in mathematics and physics. Since 1995 he is Associate Professor at the Vienna University of Technology in Austria. His research interests include array and graph grammars, regulated rewriting, infinite words, syntactic pattern recognition, neural networks, and especially models and systems for biological computing. In these fields, he is author or co-author of more than ninety scientific papers. Marion Oswald, Ph.D.: She received her master and doctor degree in computer science from the Vienna University of Technology, Austria, in 2001 and 2003, respectively. Her research interests include but are not limited to artificial life as well as models and systems for biological computing, in which fields she is author or co-author of more than fifteen scientific papers.     

The power of communication: P systems with symport/antiport

In the attempt to have a framework where the computation is done by communication only, we consider the biological phenomenon of trans-membrane transport of couples of chemicals (one say symport when two chemicals pass together through a membrane, in the same direction, and antiport when two chemicals pass simultaneously through a membrane, in opposite directions). Surprisingly enough, membrane systems without changing (evolving) the used objects and with the communication based on rules of this type are computationally complete, and this result is achieved even for pairs of communicated objects (as encountered in biology). Five membranes are used; the number of membranes is reduced to two if more than two chemicals may collaborate when passing through membranes. Andrei Paun: He graduated the Faculty of Mathematics of Bucharest University in 1998, received his M.Sc. degree from The University of Western Ontario in 1999, and since then he is a PhD student in the Computer Science Department of University of Western Ontario, London, Canada (under the guidance of prof. Sheng Yu). The topic of his thesis is Molecular Computing (especially, DNA and Membrane Computing), but his research interests also include neural networks, implementing automata, combinatorics on words. Gheorghe Paun: (the proud father of two sons, including the first author of this paper) He is a member of the Romanian Academy, working as a senior researcher in the Institute of Mathematics of the Romanian Academy, Bucharest, and as a Ramon y Cajal researcher in Rovira i Virgili University of Tarragona, Spain. He is one of the most active authors in (the theory of) DNA Computing, (co)author of many papers in this area, (co)author and (co)editor of several books. In 1998 he has initiated the area of Membrane Computing. Other research interests: regulated rewriting, grammar systems, contextual grammars, combinatorics on words, computational linguistics.     

Further remarks on P systems with active membranes, separation, merging, and release rules

The P systems are a class of distributed parallel computing devices of a biochemical type. In this note, we show that by using membrane separation to obtain exponential workspace, SAT problem can be solved in linear time in a uniform and confluent way by active P systems without polarizations. This improves some results already obtained by A. Alhazov, T.-O. Isdorj. A universality result related to membrane separation is also obtained.Dedicated to Prof. Zhang Kemin for his 70th birthday     

P systems with minimal parallelism

A current research topic in membrane computing is to find more realistic P systems from a biological point of view, and one target in this respect is to relax the condition of using the rules in a maximally parallel way. We contribute in this paper to this issue by considering the minimal parallelism of using the rules: if at least a rule from a set of rules associated with a membrane or a region can be used, then at least one rule from that membrane or region must be used, without any other restriction (e.g., more rules can be used, but we do not care how many). Weak as it might look, this minimal parallelism still leads to universality. We first prove this for the case of symport/antiport rules. The result is obtained both for generating and accepting P systems, in the latter case also for systems working deterministically. Then, we consider P systems with active membranes, and again the usual results are obtained: universality and the possibility to solve NP-complete problems in polynomial time (by trading space for time).     

Results on catalytic and evolution-communication P systems

In this paper we give several improved universality results for two important classes of P systems: P systems with catalysts and evolution-communication P systems. First, the result from Reference,¹⁴⁾ stating that six catalysts ensure the universality, has been improved in two ways: using bistable catalysts and using moving catalysts. Specifically, the universality can be reached with one bistable catalyst and 2 usual catalysts (using five membranes), as well as with one moving catalyst and three membranes, or with two moving catalysts and only two membranes. The second part of the paper deals with evolution-communication P systems, and we also give improved universality results for this type of systems, in terms of the weight of symport/antiport rules, number of membranes, or number of catalysts. Shankara Narayanan Krishna: She is an Assistant Professor in Dept. Computer Science & Engg, IIT Bombay, India. Her research interests are Natural Computing and Formal Methods. Andrei Paun, Ph.D.: He obtained his bachelor degree in Mathematics and Computer Science from the University of Bucharest, Romania. He obtaind his Ph.D. degree in Computer Science, at University of Western Ontario, Canada, under the supervision of Prof. Dr. Sheng Yu, with the thesis “Unconventional Models of Computation: DNA and Membrane Computing”. After graduation he received a postdoctoral felloship from NSERC, Canada and after six months he accepted an assistant professor position in US at Louisiana Tech University.     

Minimizing evolution-communication P systems and automata

Evolution-communication P systems are a variant of P systems allowing both rewriting rules and symport/antiport rules, thus having separated the rewriting and the communication. The purpose of this paper is to solve an open problem stated in Reference,¹⁾ namely generating the family of Turing computable sets of vectors of natural numbers instead of the family of Turing computable sets of natural numbers. The same construction also reduces the 3-membrane non-cooperative case and the 2-membrane 1-catalyst case to the 2-membrane non-cooperative case. Also, EC P automata are introduced and it is proved that 2-membrane EC P automata with a promoter can accept all recursively enumerable languages. Finally, a definition of an extended system is given, and its universality is proved using the rules of more restricted types. Artiom Alhazov: He has graduated from Mathematics and Computer Science, State University of Moldova in 2001, and is currently a Ph.D. student in Chişinăm, Moldova, and Tarragona, Spain. He has won prizes at 3 National Olympiads in Informatics and in Mathematics (1995 and 1996), participated at 8th International Olympiad in Informatics (Veszprem, Hungary, 1996). He has experience in programming and teaching, and has published 18 papers, mostly in Membrane Computing. His interests are Origami, Mathematics, Programming, Theoretical Computer Science, Formal Linguistics and Biocomputing.     

On the power and size of extended gemmating P systems

In [3] P systems with gemmation of mobile membranes were examined. It was shown that (extended) systems with eight membranes are as powerful as the Turing machines. Moreover, it was proved that extended gemmating P systems with only pre-dynamical rules are still computationally complete: in this case nine membranes are needed to obtain this computational power. In this paper we improve the above results concerning the size bound of extended gemmating P systems, namely we prove that these systems with at most five membranes (with meta-priority relations and without communication rules) form a class of universal computing devices, while in the case of extended systems with only pre-dynamical rules six membranes are enough to determine any recursively enumerable language.     

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.     

Hierarchies of parallel rewriting P systems — A survey

The paper is about some families of rewriting P systems, where the application of evolution rules is extended from the classical sequential rewriting to the parallel one (as, for instance, in Lindenmayer systems). As a result, consistency problems for the communication of strings may arise. Three variants of parallel rewriting P systems (already present in the literature) are considered here, together with the strategies they use to face the communication problem, and some parallelism methods for string rewriting are defined. We give a survey of all known results about each variant and we state some relations among the three variants, thus establishing hierarchies of parallel rewriting P systems. Various open problems related to the subject are also presented. Danicla Besozzi: She is assistant professor at the University of Milano. She received her M.S. in Mathematics (2000) from the University of Como and Ph.D. in Computer Science (2004) from the University of Milano. Her research interests cover topics in Formal Language Theory, Molecular Computing, Systems Biology. She is member of EATCS (European Association for Theoretical Computer Science) and EMCC (European Molecular Computing Consortium). Giancarlo Mauri: He is full professor of Computer Science at the University of Milano-Bicocca. His research interests are mainly in the area of theoretical computer science, and include: formal languages and automata, computational complexity, computational learning theory, soft computing techniques, cellular automata, bioinformatics and molecular computing. On these subjects, he published more than 150 scientific papers in international journals, contributed volumes and conference proceedings. Claudio Zandron: He received Ph.D. in Computer Science at the University of Milan, Italy, in 2001. Since 2002 he is assistant professor at the University of Milano-Bicocca, Italy. He is member of the EATCS (European Association for Theoretical Computer Science) and of EMCC (European Molecular Computing Consortium). His research interests are Molecular Computing (DNA and Membrane Computing) and Formal Languages.     

Region-based segmentation of 2D and 3D images with tissue-like P systems

Membrane Computing is a biologically inspired computational model. Its devices are called P systems and they perform computations by applying a finite set of rules in a synchronous, maximally parallel way. In this paper, we develop a variant of P-system, called tissue-like P system in order to design in this computational setting, a region-based segmentation algorithm of 2D pixel-based and 3D voxel-based digital images. Concretely, we use 4-adjacency neighborhood relation between pixels in 2D and 6-adjacency neighborhood relation between voxel in 3D for segmenting digital images in a constant number of steps. Finally, specific software is used to check the validity of these systems with some simple examples.     

Trading polarizations for labels in P systems with active membranes

This paper addresses the problem of removing the polarization of membranes from P systems with active membranes - and this is achieved by allowing the change of membrane labels by means of communication rules or by membrane dividing rules. As consequences of these results, we obtain the universality of P systems with active membranes which are allowed to change the labels of membranes, but do not use polarizations. Universality results are easily obtained also by direct proofs. By direct constructions, we also prove that SAT can be solved in linear time by systems without polarizations and with label changing possibilities. If non-elementary membranes can be divided, then SAT can be solved in linear time without using polarizations and label changing. Several open problems are also formulated.Received: 29 October 2003, Published online: 29 October 2004Artiom Alhazov: artiome.alhazov@estudiantsLinqiang Pan: lp@fll.urv.esGheorghe Pun: george.paun@imar.ro     

P systems with active membranes: trading time for space

We consider recognizer P systems having three polarizations associated to the membranes, and we show that they are able to solve the PSPACE-complete problem Quantified 3SAT when working in polynomial space and exponential time. The solution is uniform (all the instances of a fixed size are solved by the same P system) and uses only communication rules: evolution rules, as well as membrane division and dissolution rules, are not used. Our result shows that, as it happens with Turing machines, this model of P systems can solve in exponential time and polynomial space problems that cannot be solved in polynomial time, unless P = SPACE.