<?xml version="1.0" encoding="UTF-8"?><xml><records><record><source-app name="Biblio" version="6.x">Drupal-Biblio</source-app><ref-type>13</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Linqiang Pan</style></author><author><style face="normal" font="default" size="100%">David Orellana-Martín</style></author><author><style face="normal" font="default" size="100%">Bosheng Song</style></author><author><style face="normal" font="default" size="100%">Mario J. Pérez-Jiménez</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">Cell-like P systems with polarizations and minimal rules</style></title><secondary-title><style face="normal" font="default" size="100%">Theoretical Computer Science</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">bio-inspired computing</style></keyword><keyword><style  face="normal" font="default" size="100%">Membrane computing</style></keyword><keyword><style  face="normal" font="default" size="100%">Minimal rule</style></keyword><keyword><style  face="normal" font="default" size="100%">Universality</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2020</style></year><pub-dates><date><style  face="normal" font="default" size="100%">05/2020</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">http://www.sciencedirect.com/science/article/pii/S0304397519306231</style></url></web-urls></urls><publisher><style face="normal" font="default" size="100%">Elsevier</style></publisher><pub-location><style face="normal" font="default" size="100%">Amsterdam (The Netherlands)</style></pub-location><volume><style face="normal" font="default" size="100%">816</style></volume><pages><style face="normal" font="default" size="100%">1-18</style></pages><abstract><style face="normal" font="default" size="100%">P systems with active membranes are a class of computation models in the area of membrane computing, which are inspired from the mechanism by which chemicals interact and cross cell membranes. In this work, we consider a normal form of P systems with active membranes, called cell-like P systems with polarizations and minimal rules, where rules are minimal in the sense that an object evolves to exactly one object with the application of an evolution rule or a communication rule, or an object evolves to two objects that are assigned to the two new generated membranes by applying a division rule. The present work investigates the computational power of P systems with polarizations and minimal rules. Specifically, results about Turing universality and non-universality are obtained with the combination of the number of membranes, the number of polarizations, and the types of rules. We also show that polarizationless P systems with minimal rules are equivalent to Turing machines working in a polynomial space, that is, the class of problems that can be solved in polynomial time by polarizationless P systems with minimal rules is equal to the class PSPACE.</style></abstract></record><record><source-app name="Biblio" version="6.x">Drupal-Biblio</source-app><ref-type>13</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Bosheng Song</style></author><author><style face="normal" font="default" size="100%">Linqiang Pan</style></author><author><style face="normal" font="default" size="100%">Mario J. Pérez-Jiménez</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">Tissue P Systems with Protein on Cells</style></title><secondary-title><style face="normal" font="default" size="100%">Fundamenta Informaticae</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">bio-inspired computing</style></keyword><keyword><style  face="normal" font="default" size="100%">cell division</style></keyword><keyword><style  face="normal" font="default" size="100%">Cell protein</style></keyword><keyword><style  face="normal" font="default" size="100%">Membrane computing</style></keyword><keyword><style  face="normal" font="default" size="100%">Tissue P System</style></keyword><keyword><style  face="normal" font="default" size="100%">Universality</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2016</style></year><pub-dates><date><style  face="normal" font="default" size="100%">03/2016</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">http://content.iospress.com/articles/fundamenta-informaticae/fi1324</style></url></web-urls></urls><publisher><style face="normal" font="default" size="100%">IOS Press</style></publisher><pub-location><style face="normal" font="default" size="100%">Warsaw, Poland</style></pub-location><volume><style face="normal" font="default" size="100%">144</style></volume><pages><style face="normal" font="default" size="100%">77-107</style></pages><abstract><style face="normal" font="default" size="100%">Tissue P systems are a class of distributed parallel computing devices inspired by biochemical interactions between cells in a tissue-like arrangement, where objects can be exchanged by means of communication channels. In this work, inspired by the biological facts that the movement of most objects through communication channels is controlled by proteins and proteins can move through lipid bilayers between cells (if these cells are fused), we present a new class of variant tissue P systems, called tissue P systems with protein on cells, where multisets of objects (maybe empty), together with proteins between cells are exchanged. The computational power of such P systems is studied. Specifically, an efficient (uniform) solution to the SAT problem by using such P systems with cell division is presented. We also prove that any Turing computable set of numbers can be generated by a tissue P system with protein on cells. Both of these two results are obtained by such P systems with communication rules of length at most 4 (the length of a communication rule is the total number of objects and proteins involved in that rule).</style></abstract><issue><style face="normal" font="default" size="100%">1</style></issue><custom1><style face="normal" font="default" size="100%">0.717</style></custom1><custom2><style face="normal" font="default" size="100%">71/104 - Q3</style></custom2></record><record><source-app name="Biblio" version="6.x">Drupal-Biblio</source-app><ref-type>13</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Bosheng Song</style></author><author><style face="normal" font="default" size="100%">Mario J. Pérez-Jiménez</style></author><author><style face="normal" font="default" size="100%">Linqiang Pan</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">Computational efficiency and universality of timed P systems with membrane creation</style></title><secondary-title><style face="normal" font="default" size="100%">Soft Computing</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">Membrane creation</style></keyword><keyword><style  face="normal" font="default" size="100%">P system</style></keyword><keyword><style  face="normal" font="default" size="100%">SAT problem</style></keyword><keyword><style  face="normal" font="default" size="100%">Time-free solution</style></keyword><keyword><style  face="normal" font="default" size="100%">Universality</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2015</style></year><pub-dates><date><style  face="normal" font="default" size="100%">11/2015</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">http://link.springer.com/article/10.1007%2Fs00500-015-1732-3</style></url></web-urls></urls><publisher><style face="normal" font="default" size="100%">Springer Verlag</style></publisher><pub-location><style face="normal" font="default" size="100%">Berlin, Germany</style></pub-location><volume><style face="normal" font="default" size="100%">19</style></volume><pages><style face="normal" font="default" size="100%">3043-3053</style></pages><abstract><style face="normal" font="default" size="100%">P systems are a class of distributed parallel computing models inspired by the structure and the functioning of a living cell, where the execution of each rule is completed in exactly one time unit (a global clock is assumed). However, in living cells, the execution time of different biological processes is difficult to know precisely and very sensitive to environmental factors that might be hard to control. Inspired from this biological motivation, in this work, timed polarization P systems with membrane creation are introduced and their computational efficiency and universality are investigated. Specifically, we give a time-free semi-uniform solution to the SAT problem by a family of P systems with membrane creation in the sense that the correctness of the solution is irrelevant to the times associated with the involved rules. We also prove that time-free P systems with membrane creation are computationally universal.</style></abstract><issue><style face="normal" font="default" size="100%">11</style></issue><custom1><style face="normal" font="default" size="100%">1.271</style></custom1><custom2><style face="normal" font="default" size="100%">65/123 - Q3</style></custom2></record><record><source-app name="Biblio" version="6.x">Drupal-Biblio</source-app><ref-type>13</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Gheorghe Paun</style></author><author><style face="normal" font="default" size="100%">Mario J. Pérez-Jiménez</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">Towards bridging two cell-inspired models: P systems and R systems</style></title><secondary-title><style face="normal" font="default" size="100%">Theoretical Computer Science</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">Membrane computing</style></keyword><keyword><style  face="normal" font="default" size="100%">P system</style></keyword><keyword><style  face="normal" font="default" size="100%">Reaction system (R system)</style></keyword><keyword><style  face="normal" font="default" size="100%">Universality</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2012</style></year></dates><urls><web-urls><url><style face="normal" font="default" size="100%">http://www.sciencedirect.com/science/article/pii/S0304397511010127</style></url></web-urls></urls><publisher><style face="normal" font="default" size="100%">Elsevier</style></publisher><pub-location><style face="normal" font="default" size="100%">Amsterdam (The Netherlands)</style></pub-location><volume><style face="normal" font="default" size="100%">429</style></volume><pages><style face="normal" font="default" size="100%">258-264</style></pages><abstract><style face="normal" font="default" size="100%">We examine, from the point of view of membrane computing, the two basic assumptions of reaction systems, the “threshold” and “no permanence” ones. In certain circumstances (e.g., defining the successful computations by local halting), the second assumption can be incorporated in a transition P system or in a symport/antiport P system without losing the universality. The case of the first postulate remains open: the reaction systems deal, deterministically, with finite sets of symbols, which is not of much interest for computing; three ways to introduce nondeterminism are suggested and left as research topics.</style></abstract><custom1><style face="normal" font="default" size="100%">0.489</style></custom1><custom2><style face="normal" font="default" size="100%">78/100 - Q4</style></custom2></record><record><source-app name="Biblio" version="6.x">Drupal-Biblio</source-app><ref-type>13</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Oscar Ibarra</style></author><author><style face="normal" font="default" size="100%">Mario J. Pérez-Jiménez</style></author><author><style face="normal" font="default" size="100%">Takashi Yokomori</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">On spiking neural P systems</style></title><secondary-title><style face="normal" font="default" size="100%">Natural Computing</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">Asynchronous</style></keyword><keyword><style  face="normal" font="default" size="100%">Finite automaton</style></keyword><keyword><style  face="normal" font="default" size="100%">Finite state transducer</style></keyword><keyword><style  face="normal" font="default" size="100%">Formal Verification</style></keyword><keyword><style  face="normal" font="default" size="100%">Sequential</style></keyword><keyword><style  face="normal" font="default" size="100%">Spiking neural P system</style></keyword><keyword><style  face="normal" font="default" size="100%">Systolic trellis automaton</style></keyword><keyword><style  face="normal" font="default" size="100%">Universality</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2010</style></year><pub-dates><date><style  face="normal" font="default" size="100%">06/2010</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">http://www.springerlink.com/content/krhu646461138370/</style></url></web-urls></urls><publisher><style face="normal" font="default" size="100%">Springer Verlag</style></publisher><pub-location><style face="normal" font="default" size="100%">Amsterdam, Netherlands</style></pub-location><volume><style face="normal" font="default" size="100%">9</style></volume><pages><style face="normal" font="default" size="100%">475-491</style></pages><abstract><style face="normal" font="default" size="100%">This work deals with several aspects concerning the formal verification of SN P systems and the computing power of some variants. A methodology based on the information given by the transition diagram associated with an SN P system is presented. The analysis of the diagram cycles codifies invariants formulae which enable us to establish the soundness and completeness of the system with respect to the problem it tries to resolve. We also study the universality of asynchronous and sequential SN P systems and the capability these models have to generate certain classes of languages. Further, by making a slight modification to the standard SN P systems, we introduce a new variant of SN P systems with a special I/O mode, called SN P modules, and study their computing power. It is demonstrated that, as string language acceptors and transducers, SN P modules can simulate several types of computing devices such as finite automata, a-finite transducers, and systolic trellis automata.</style></abstract><issue><style face="normal" font="default" size="100%">2</style></issue></record><record><source-app name="Biblio" version="6.x">Drupal-Biblio</source-app><ref-type>13</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Haiming Chen</style></author><author><style face="normal" font="default" size="100%">Mihai Ionescu</style></author><author><style face="normal" font="default" size="100%">Tseren-Onolt Ishdorj</style></author><author><style face="normal" font="default" size="100%">Andrei Paun</style></author><author><style face="normal" font="default" size="100%">Gheorghe Paun</style></author><author><style face="normal" font="default" size="100%">Mario J. Pérez-Jiménez</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">Spiking Neural P systems with extended rules: universality and languages</style></title><secondary-title><style face="normal" font="default" size="100%">Natural Computing</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">chomsky hierarchy</style></keyword><keyword><style  face="normal" font="default" size="100%">Membrane computing</style></keyword><keyword><style  face="normal" font="default" size="100%">spiking neural P systems</style></keyword><keyword><style  face="normal" font="default" size="100%">Turing computability</style></keyword><keyword><style  face="normal" font="default" size="100%">Universality</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2008</style></year><pub-dates><date><style  face="normal" font="default" size="100%">06/2008</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">http://dx.doi.org/10.1007/s11047-006-9024-6</style></url></web-urls></urls><publisher><style face="normal" font="default" size="100%">Springer Netherlands</style></publisher><volume><style face="normal" font="default" size="100%">7</style></volume><pages><style face="normal" font="default" size="100%">147-166</style></pages><abstract><style face="normal" font="default" size="100%">We consider spiking neural P systems with rules allowed to introduce zero, one, or more spikes at the same time. The motivation comes both from constructing small universal systems and from generating strings; previous results from these areas are briefly recalled. Then, the computing power of the obtained systems is investigated, when considering them as number generating and as language generating devices. In the first case, a simpler proof of universality is obtained, while in the latter case we find characterizations of finite and recursively enumerable languages (without using any squeezing mechanism, as it was necessary in the case of standard rules). The relationships with regular languages are also investigated.</style></abstract><issue><style face="normal" font="default" size="100%">2</style></issue></record><record><source-app name="Biblio" version="6.x">Drupal-Biblio</source-app><ref-type>13</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Oscar Ibarra</style></author><author><style face="normal" font="default" size="100%">Andrei Paun</style></author><author><style face="normal" font="default" size="100%">Gheorghe Paun</style></author><author><style face="normal" font="default" size="100%">Alfonso Rodríguez-Patón</style></author><author><style face="normal" font="default" size="100%">Petr Sosik</style></author><author><style face="normal" font="default" size="100%">Sara Woodworth</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">Normal forms for spiking neural P systems</style></title><secondary-title><style face="normal" font="default" size="100%">Theoretical Computer Science</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">Membrane computing</style></keyword><keyword><style  face="normal" font="default" size="100%">normal form</style></keyword><keyword><style  face="normal" font="default" size="100%">Spiking neural P system</style></keyword><keyword><style  face="normal" font="default" size="100%">Universality</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2007</style></year><pub-dates><date><style  face="normal" font="default" size="100%">03/2007</style></date></pub-dates></dates><urls><web-urls><url><style face="normal" font="default" size="100%">http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6V1G-4MG065P-4&_user=10&_coverDate=03%2F15%2F2007&_rdoc=1&_fmt=high&_orig=search&_sort=d&_docanchor=&view=c&_searchStrId=1258622819&_rerunOrigin=google&_acct=C000050221&_version=1&_urlVersion=0&_us</style></url></web-urls></urls><publisher><style face="normal" font="default" size="100%">Elsevier</style></publisher><pub-location><style face="normal" font="default" size="100%">Amsterdam (The Netherlands)</style></pub-location><volume><style face="normal" font="default" size="100%">372</style></volume><pages><style face="normal" font="default" size="100%">196-217</style></pages><abstract><style face="normal" font="default" size="100%">The spiking neural P systems are a class of computing devices recently introduced as a bridge between spiking neural nets and membrane computing. In this paper we prove a series of normal forms for spiking neural P systems, concerning the regular expressions used in the firing rules, the delay between firing and spiking, the forgetting rules used, and the outdegree of the graph of synapses. In all cases, surprising simplifications are found, without losing the computational completeness — sometimes at the price of (slightly) increasing other parameters which describe the complexity of these systems.</style></abstract><issue><style face="normal" font="default" size="100%">2-3</style></issue></record><record><source-app name="Biblio" version="6.x">Drupal-Biblio</source-app><ref-type>13</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Gheorghe Paun</style></author><author><style face="normal" font="default" size="100%">Radu  Paun</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">Membrane Computing and Economics: Numerical P Systems</style></title><secondary-title><style face="normal" font="default" size="100%">Fundamenta Informaticae</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">economics</style></keyword><keyword><style  face="normal" font="default" size="100%">Membrane computing</style></keyword><keyword><style  face="normal" font="default" size="100%">Turing computability</style></keyword><keyword><style  face="normal" font="default" size="100%">Universality</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2006</style></year></dates><urls><web-urls><url><style face="normal" font="default" size="100%">http://portal.acm.org/citation.cfm?id=1231159.1231179&coll=GUIDE&dl=GUIDE&CFID=1691426&CFTOKEN=24108515</style></url></web-urls></urls><publisher><style face="normal" font="default" size="100%">IOS Press</style></publisher><pub-location><style face="normal" font="default" size="100%">Warsaw, Poland</style></pub-location><volume><style face="normal" font="default" size="100%">73</style></volume><pages><style face="normal" font="default" size="100%">213-227</style></pages><abstract><style face="normal" font="default" size="100%">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.

</style></abstract><issue><style face="normal" font="default" size="100%">1-2</style></issue></record><record><source-app name="Biblio" version="6.x">Drupal-Biblio</source-app><ref-type>13</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Gheorghe Paun</style></author><author><style face="normal" font="default" size="100%">Mario J. Pérez-Jiménez</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">Membrane Computing: Brief introduction, recent results and applications.</style></title><secondary-title><style face="normal" font="default" size="100%">BioSystems</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">EGFR signalling network</style></keyword><keyword><style  face="normal" font="default" size="100%">Membrane computing</style></keyword><keyword><style  face="normal" font="default" size="100%">Multiset processing</style></keyword><keyword><style  face="normal" font="default" size="100%">Natural computing</style></keyword><keyword><style  face="normal" font="default" size="100%">Universality</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2006</style></year></dates><urls><web-urls><url><style face="normal" font="default" size="100%">http://www.sciencedirect.com/science?_ob=ArticleURL&_udi=B6T2K-4JVSWWG-1&_user=603129&_coverDate=07%2F31%2F2006&_rdoc=1&_fmt=&_orig=search&_sort=d&view=c&_acct=C000031118&_version=1&_urlVersion=0&_userid=603129&md5=0debc4b4b403eae0151f31da581114e7</style></url></web-urls><related-urls><url><style face="normal" font="default" size="100%">http://www.gcn.us.es/files/Biosystems.pdf</style></url></related-urls></urls><pub-location><style face="normal" font="default" size="100%">The Netherlands</style></pub-location><volume><style face="normal" font="default" size="100%">85</style></volume><pages><style face="normal" font="default" size="100%">11-22</style></pages><abstract><style face="normal" font="default" size="100%">The internal organization and functioning of living cells, as well as their cooperation in tissues and higher order structures, can be a rich source of inspiration for computer science, not fully exploited at the present date. Membrane computing is an answer to this challenge, well developed at the theoretical (mathematical and computability theory) level, already having several applications (via usual computers), but without having yet a bio-lab implementation. After briefly discussing some general issues related to natural computing, this paper provides an informal introduction to membrane computing, focused on the main ideas, the main classes of results and of applications. Then, three recent achievements, of three different types, are briefly presented, with emphasis on the usefulness of membrane computing as a framework for devising models of interest for biological and medical research. 
</style></abstract><issue><style face="normal" font="default" size="100%">1</style></issue></record><record><source-app name="Biblio" version="6.x">Drupal-Biblio</source-app><ref-type>13</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Gheorghe Paun</style></author><author><style face="normal" font="default" size="100%">Yasuhiro Suzuki</style></author><author><style face="normal" font="default" size="100%">Hiroshi Tanaka</style></author><author><style face="normal" font="default" size="100%">Takashi Yokomori</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">On the power of membrane division in P systems</style></title><secondary-title><style face="normal" font="default" size="100%">Theoretical Computer Science</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">Membrane computing</style></keyword><keyword><style  face="normal" font="default" size="100%">recursively enumerable language</style></keyword><keyword><style  face="normal" font="default" size="100%">SAT problem</style></keyword><keyword><style  face="normal" font="default" size="100%">Universality</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2004</style></year></dates><urls><web-urls><url><style face="normal" font="default" size="100%">http://portal.acm.org/citation.cfm?id=1041011</style></url></web-urls></urls><publisher><style face="normal" font="default" size="100%">Elsevier</style></publisher><pub-location><style face="normal" font="default" size="100%">Amsterdam (The Netherlands)</style></pub-location><volume><style face="normal" font="default" size="100%">324</style></volume><pages><style face="normal" font="default" size="100%">61 - 85</style></pages><abstract><style face="normal" font="default" size="100%">First, we consider P systems with active membranes, hence with the possibility that the membranes can be divided, with non-cooperating evolution rules (the objects always evolve separately). These systems are known to be able to solve NP-complete problems in linear time. Here we give a normal form theorem for such systems: their computational universality is preserved even if only the elementary membranes are divided. The possibility of solving SAT in linear time is preserved only when non-elementary membranes may also be divided under the influence of objects in their region.Second, we consider a slight generalization, namely, we allow that a membrane can produce by division both a copy of itself and a copy of a membrane with a different label; again, only elementary membranes may be divided. In this case, we prove that the hierarchy on the maximal number of membranes present in the system collapses: three membranes at a time are sufficient in order to characterize the recursively enumerable sets of vectors of natural numbers. This result is optimal, two membranes are shown not to be sufficient.Third, we consider P systems with cooperating rules (several objects may evolve together). Making use of this powerful feature, we show that many NP-complete problems can be solved in linear time in a quite uniform way (by systems which are very similar to each other), using only elementary membranes division (and not further ingredients, such as electrical charges). The degree of cooperation is minimal: two objects at a time. 


</style></abstract><issue><style face="normal" font="default" size="100%">1</style></issue></record><record><source-app name="Biblio" version="6.x">Drupal-Biblio</source-app><ref-type>13</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Adam Obtulowicz</style></author><author><style face="normal" font="default" size="100%">Gheorghe Paun</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">(In search of) probabilistic P systems </style></title><secondary-title><style face="normal" font="default" size="100%">Biosystems</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">Biochemistry</style></keyword><keyword><style  face="normal" font="default" size="100%">Membrane computing</style></keyword><keyword><style  face="normal" font="default" size="100%">Probability</style></keyword><keyword><style  face="normal" font="default" size="100%">Turing computability</style></keyword><keyword><style  face="normal" font="default" size="100%">Universality</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2003</style></year></dates><urls><web-urls><url><style face="normal" font="default" size="100%">http://www.ingentaconnect.com/content/els/03032647/2003/00000070/00000002/art00034</style></url></web-urls></urls><publisher><style face="normal" font="default" size="100%">Elsevier</style></publisher><pub-location><style face="normal" font="default" size="100%">San Diego, CA, USA</style></pub-location><volume><style face="normal" font="default" size="100%">70</style></volume><pages><style face="normal" font="default" size="100%">107-121</style></pages><abstract><style face="normal" font="default" size="100%">The aim of this paper is to (preliminarily) discuss various ways of introducing probabilities in membrane systems. We briefly present both ideas already circulated in the literature and new proposals, trying to have a systematic overview of possibilities of associating probabilities with the ingredients of a membrane system: with (localization of) single objects, with multiplicities of objects (hence with the multisets), with the rules (depending or not on the previous applied rule), with the communication targets. For a certain mode of using the probabilities associated with the evolution rules (in string-object P systems) we obtain the computational universality.

</style></abstract><issue><style face="normal" font="default" size="100%">2</style></issue></record><record><source-app name="Biblio" version="6.x">Drupal-Biblio</source-app><ref-type>13</ref-type><contributors><authors><author><style face="normal" font="default" size="100%">Daniela Besozzi</style></author><author><style face="normal" font="default" size="100%">Giancarlo Mauri</style></author><author><style face="normal" font="default" size="100%">Gheorghe Paun</style></author><author><style face="normal" font="default" size="100%">Claudio Zandron</style></author></authors></contributors><titles><title><style face="normal" font="default" size="100%">Gemmating P systems: collapsing hierarchies </style></title><secondary-title><style face="normal" font="default" size="100%">Theoretical Computer Science</style></secondary-title></titles><keywords><keyword><style  face="normal" font="default" size="100%">matrix grammar</style></keyword><keyword><style  face="normal" font="default" size="100%">Membrane computing</style></keyword><keyword><style  face="normal" font="default" size="100%">recursively enumerable languages</style></keyword><keyword><style  face="normal" font="default" size="100%">Universality</style></keyword></keywords><dates><year><style  face="normal" font="default" size="100%">2003</style></year></dates><urls><web-urls><url><style face="normal" font="default" size="100%">http://linkinghub.elsevier.com/retrieve/pii/S0304397502006576</style></url></web-urls></urls><publisher><style face="normal" font="default" size="100%">Elsevier</style></publisher><pub-location><style face="normal" font="default" size="100%">Amsterdam (The Netherlands)</style></pub-location><volume><style face="normal" font="default" size="100%">296</style></volume><pages><style face="normal" font="default" size="100%">253-267 </style></pages><abstract><style face="normal" font="default" size="100%">We continue the analysis of P systems with gemmation of mobile membranes. We solve an open problem from Besozzi et al. (Proc. Italian Conf. on Theoretical Computer Science 2001, Lecture Notes in Computer Science, Vol. 2202, Springer, Berlin, 2001, pp. 136–153), showing that the hierarchy on the number of membranes collapses: systems with eight membranes characterize the recursively enumerable languages (seven membranes are enough in the case of extended systems). We also prove that P systems, which use only gemmation, but neither classical rewriting rules nor in/out communications, can generate the same family of languages. In this case, the hierarchy on the number of membranes collapses to level nine. 

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