## Introduction to Membrane Computing

Citations: | 98 - 6 self |

### BibTeX

@MISC{Păun_introductionto,

author = {Gheorghe Păun},

title = { Introduction to Membrane Computing},

year = {}

}

### OpenURL

### Abstract

### Citations

614 | Molecular computation of solutions to combinatorial problems
- Adleman
- 1994
(Show Context)
Citation Context ...d yet computational applicability (we do not discuss here the by-products, such as the nanotechnology related developments), is DNA computing, whose birth certificate is related to Adleman experiment =-=[1]-=- of solving a (small) instance of the Hamiltonian path problem by handling DNA molecules in a laboratory. According to Hartmanis [50], [51], it was a demo that we can compute with bio-molecules, a big... |

454 | Computation: finite and infinite machines - Minsky - 1967 |

344 | Computing with membranes - Păun - 1998 |

189 |
Formal Language Theory and DNA: an analysis of the generative capacity of specific recombinant behaviors
- Head
- 1987
(Show Context)
Citation Context ... information promises to be useful in solving computationally hard problems in a feasible time. Actually, at the theoretical level one can say that DNA computing started already in 1987, when T. Head =-=[49]-=- has proposed a language theoretic model of what he called the splicing operation (the recombination of DNA molecules, cut by restriction enzymes in fragments pasted together when the sticky ends matc... |

178 |
Foundations of Systems Biology
- Kitano
- 2001
(Show Context)
Citation Context ... direct interest for bi ology. Actually, this last statement is not at all correct: if a biologist is interested in simulating a cell – and this seems to become a major concern of to-day biology, see =-=[58]-=-, [53] and other sources – t hen the generality of the model (its comparison with Turing machines and its restrictions) is directly linked to the possibility of solving algorithmically questions about... |

168 | Shapiro: BioAmbients – An Abstraction for Biological Compartments - Regev, Panina, et al. |

81 | DNA Computing: New Computing Paradigms - Paun, Rozenberg, et al. - 1999 |

73 | Computing with Membranes. An Introduction - Păun - 2002 |

68 | Păun: The Power of Communication: P Systems with Symport/Antiport - Păun, Gh |

58 |
Métayer: A Parallel Machine for Multiset Transformation and Its Programming Style. Future Generation Computer Systems
- Banâtre, Coutant, et al.
- 1988
(Show Context)
Citation Context ...al parallelism – we process as many objects as possible, but not necessari ly all of them. Still closer to membrane computing are the multiset processing languages, the most known of them being Gamma =-=[9, 10]-=-. The standard rules of Gamma are of the form u → v(π), where u and v ar e multisets and π is a predicate which should be satisfied by the multiset to which the rule u → v is applied. The generality o... |

50 |
Remarks on Blind and Partially Blind One-Way Multicounter Machines
- Greibach
- 1978
(Show Context)
Citation Context ...iversal even when using only three objects). In turn, two objects ( but without a bound on the number of membranes) are sufficient in order to generate all sets of vectors com puted by so-called (see =-=[46]-=-) partially blind counter machines (for sets of numbers the result is not so interesting, because partially blind counter machines accept only semilinear sets of numbers, while t he sets of vectors th... |

48 | P Systems with Active Membranes: Attacking NP-Complete Problems - Păun |

36 | Whole–Cell Simulation: A Grand Challenge of the 21st Century - Tomita |

34 |
On the Weight of Computation
- Hartmanis
- 1995
(Show Context)
Citation Context ...ing, whose birth certificate is related to Adleman experiment [1] of solving a (small) instance of the Hamiltonian path problem by handling DNA molecules in a laboratory. According to Hartmanis [50], =-=[51]-=-, it was a demo that we can compute with bio-molecules, a big event for computability. However, after one decade of research, the domain is still preparing its tools for a possible future practical ap... |

33 | Boudol: The Chemical Abstract Machine - Berry, G - 1992 |

32 |
Gheorghe: Population P Systems
- Bernardini, M
(Show Context)
Citation Context ...e halting configurat ion. A still more elaborated class of systems, called population P systems, were investigated in the last time in a series of papers by F. Bernardini and M. Gheorghe – see, e.g., =-=[14]-=- – with motivations related to the dynamics of cells in skin-like tissues, populations of bacteria, colonies of ants. These systems are highly dynamical; not only the links between cells, correspondin... |

27 |
Pérez-Jiménez: Tissue-Like P Systems with ChannelStates. Brainstorming Week on Membrane Computing
- Păun
(Show Context)
Citation Context ...er. When halting, we count the objects from a specified cell, and this is the result of the computation. The graph plays a more important role in so-called tissue-like P systems wi th channel-states, =-=[41]-=-, which are constructs of the form Π = (O, T, K, w1, . . . , wm, E, syn, (s (i,j)) (i,j)∈syn, (R (i,j)) (i,j)∈syn, io), where O is the alphabet of objects, T ⊆ O is the alphabet of terminal objects, K... |

24 | Sancho-Caparrini: Teoría de la Complejidad en Modelos de Computatión Celular con Membranas. Editorial Kronos - Pérez-Jiménez, Romero-Jiménez, et al. - 2002 |

23 | From Cells to Computers: Computing with Membranes - Păun |

23 | Solving NPComplete Problems Using P Systems with Active Membranes". Unconventional Models of Computation - Zandron, Claudio, et al. - 2000 |

21 | Rodríguez-Patón: Tissue P Systems - Păun, A |

18 | Membrane Systems with Symport/Antiport: Universality Results
- Freund, Păun
- 2003
(Show Context)
Citation Context ...t to generate only numbers (1-dimensional vectors), then we have the result of a computation in counter 1, and the set of numbers co mputed by M in this way is denoted by N(M). It is known (see [73], =-=[40]-=-) that non-determi nistic counter machines with k + 2 counters can compute any set of Turing computable k-dimensional vectors of nat ural numbers (hence machines with three counters generate exactly t... |

17 |
Wenyuan: P Systems Running on a Cluster of Computers
- Ciobanu, G
- 2003
(Show Context)
Citation Context ...e implemented, at least in principle, on the usual electronic computer – but which can be implemented on a dedicated , reconfigurable, hardware, as done in [88], or on a local network, as reported in =-=[32]-=- and [96]. This does not mean that simulations of P systems on usual comp uters are not useful; actually, such 35sprograms were used in all biological applications mentioned above , and can also have ... |

16 |
Evolution-Communication P Systems
- Cavaliere
(Show Context)
Citation Context ...ons associated with the objects from v, as well as symport/antiport rules for communicating the ob jects among compartments. Such systems, called evolution–communication P systems, were considered in =-=[23]-=- (for various restricted types of rules of the two forms). Here we do not go into this direction, but we stay closer both to the chronologi cal evolution of the domain, and to the mathematical minimal... |

15 |
Sburlan: Time-Independent P Systems
- Cavaliere, D
(Show Context)
Citation Context ...e same set of numbers irrespective which is the time f unction which associates durations with its rules? Such questions are addressed in a series of papers by M. Cavali ere and D. Sburlan; see e.g., =-=[27]-=-, [28]. Another powerful idea explored by M. Cavaliere and his collaborators is that of coupling a 32ssimple bio-inspired system, Sys, such as a P system without a large computing power, with an obser... |

13 |
Solving a PSPACE-Complete Problem by P Systems with Restricted Active Membranes
- Alhazov, Martín-Vide, et al.
(Show Context)
Citation Context ...s which can be solved in polynomial time by P systems with the possibility of dividing both elementary and non-elementary membranes. The PSPACE-complete problem used in this proof was QSAT (see [92], =-=[5]-=- for details). There also are many open problems in this area. We have mentioned already the intriguing question whether polynomial solutions to NP-complete problems can be obtained through P sys tems... |

13 | Contextual Grammars - Marcus - 1997 |

12 |
Manca: Dynamical Aspects of P Systems
- Bernardini, V
(Show Context)
Citation Context ...(b, tar2) start from the same region, and can go into different directions, one up and one down in the membrane structure. We have left in the end one of the most general type of rules, introduced in =-=[15]-=- under the name of boundary rules, directly capturing the idea that many reactions take pl ace on the inner membranes of a cell, maybe depending on the contents of both the inner and the o uter region... |

12 | Rodríguez-Patón: Symport/Antiport P Systems with Three Objects Are Universal - Păun, Pérez-Jiménez, et al. |

11 |
Vaszil: P Automata or Purely Communicating Accepting P Systems
- Csuhaj-Varju, G
(Show Context)
Citation Context ...rings of the accepted string). Similar strategies can be followed for all types of systems, tissue-like and neural-like included (but P automata were first introduced in the symport/antiport case, in =-=[37]-=- – see also [39]). The above set Na(Π) was defined in general, for non-deterministic systems, but, clearly, in the accepting mode the determinism can be imposed (the non-determinism is moved to the en... |

11 | Surfaces Inside Surfaces. On the Origin of Agency and Life - Hoffmeyer - 1998 |

11 | Teuscher: A Hardware Membrane System - Petreska, C |

9 | On the Efficiency of P Systems with Active Membranes and Two Polarizations
- Alhazov, Freund
(Show Context)
Citation Context ...ed. This can be done if other ingredients are considered, such as label changing or division of non-elementary membranes, but without adding such features the best result obtained so far is that from =-=[3]-=- where it is proved that the number of polarizations can be reduced to two. 14 A Panoply of Possibilities for Having a Dynamical Membrane Structure Membrane dissolving and dividing are only two of the... |

9 |
Computational and Modeling Power of P Systems
- Besozzi
- 2004
(Show Context)
Citation Context ... is created with a label of the form @h2 , which indicates that it is a temporary membrane, having to get dissol ved inside the membrane with label h2. Corresponding to the situation from biology, in =-=[17]-=-, [18] one considers only the case where the membranes h1, h2 are adjacent, and directly placed in the skin membrane, but the operation can be generalized. 22 bsAnyway, a gemmation rule is of the form... |

8 |
State transition dynamics: basic concepts and molecular computing perspectives
- Manca, Franco, et al.
- 2005
(Show Context)
Citation Context ... differential equations). A real program of defining discrete dynamical systems, with direct application to the dynamics of P systems, was started by V. Manca and his collaborators; we refer to [19], =-=[68]-=-, [67], [15], etc. for details. 22 Recent Developments Of course, the specification “recent” is risky, as it can soon become obsolete, but still we want to mention here some directions of research and... |

7 | Evolution and Observation – A New Way to Look at Membrane Systems
- Cavaliere, Leupold
(Show Context)
Citation Context ...couple (Sys, Obs), for various simple systems and multiset processing finite automata, proved to be a very powerful computing device, universal even for very weak systems Sys. Details can be found in =-=[24]-=-, [25]. An idea recently explored is that of trying to bound the number of objects used in a P system, and still computing all Turing computable numbers. The question can be seen as “orthogona l” on t... |

7 | Simulating the Fredkin Gate with EnergyBased P systems
- Leporati, Zandron, et al.
(Show Context)
Citation Context ...ich we only list here concern t he reversibility of computations in P systems [63], energy accounting (associating quanta of energy to objects or to rules, handled during the computation) [43], [42], =-=[62]-=-, relations with grammar systems and w ith colonies [83], descriptional complexity, non-discrete multisets [74], [34]. We close this section by mentioning the notion of the Sevilla carpet intro duced ... |

6 |
Available membrane computing software
- Gutiérrez–Naranjo, Pérez–Jiménez, et al.
(Show Context)
Citation Context ..., and can also have important didactic and research applications. An overview of membrane computing software reported in literature (some programs are available in the web page [102]) can be found in =-=[48]-=-. 24 Closing Remarks The present paper should be seen only as a general overview of membrane computin g, with the choice of topics intended to be as pertinent as possible, but, of course, not complete... |

6 | The Number of Membranes Matters - Ibarra |

6 |
Bridging P Systems and Genomics: A Preliminary Approach
- Marcus
(Show Context)
Citation Context ...alidity of this assertion browsing, e.g., through [2], [64], [8]. Life means surfaces inside surfaces, as can be learned already from the ti tle of [52], while S. Marcus puts it in an equational form =-=[69]-=-: Life = DNA software + membrane hardware. Then, there are cells living alone (unicellular organisms, such as ciliates, bac teria, etc.), but in general the cells are organized in tissues, organs, org... |

6 | S¸tefănescu: Sevilla Carpets Associated with P Systems - Păun |

5 |
Linguistic Membrane Systems and Applications
- Enguix, Lopez
(Show Context)
Citation Context ...mbrane finds the shortest path from the region where it is created to the target region). Several other operations with membranes were considered, e.g., in the context of applications to linguistics, =-=[13]-=-, as well as in [57], and in other papers, but we do not ente r into further details here. 15 Structuring the Objects In the previous classes of P systems, the objects were considered atomic, identi f... |

5 |
and G#rard Boudol. The chemical abstract machine
- Berry
- 1992
(Show Context)
Citation Context ...r hand , in search of mathematically simple and elegant models. Also membranes appear, even in Gamma related models, and this is the case with CHAM, the Chemical Abstract Machine of Berry and Boudol, =-=[16]-=-, the direct ancestor of membrane systems – wit h the mentioning that the membranes of CHAM . . . are not membranes as in the cell biology, but they correspond to the contents of membranes, multisets ... |

5 |
P Systems with Replicated Rewriting
- Krishna, Rama
(Show Context)
Citation Context ... halting computations. We do not give here an example of a rewriting or a splicing P system, but we pas s to introducing an important extension of rewriting rules, namely, rewriting with replication, =-=[60]-=-. In such systems, the rules are of the form a → (u1, tar1)||(u2, tar2)|| . . . ||(un, tarn), with the me aning that by rewriting a string x1ax1 we get n strings, x1u1x2, x1u2x2, . . . , x1unx2, whic ... |

5 |
The Touchstone of Life. Molecular Information, Cell Communication, and the Foundations of Life
- Loewenstein
- 1999
(Show Context)
Citation Context ...on surfaces”. Anyway, biology contains many fascinating facts fr om a computer science point of view, and the reader is encouraged to check the validity of this assertion browsing, e.g., through [2], =-=[64]-=-, [8]. Life means surfaces inside surfaces, as can be learned already from the ti tle of [52], while S. Marcus puts it in an equational form [69]: Life = DNA software + membrane hardware. Then, there ... |

5 | String Rewriting and Metabolism. A Logical Perspective
- Manca
- 1998
(Show Context)
Citation Context ... for investigating the processes taking place on membranes and with membranes of a cell . The idea of devising a computing device based on compartmentalization through membranes was also suggested in =-=[66]-=-. Many related areas and many roots, with many common ideas and many differences. In some extent, membrane computing is a synthesis of part of these ideas, integrated in a framework directly inspired ... |

5 | Sabadini: P Systems with Gemmation of Mobile Membranes - Besozzi, Zandron, et al. - 2001 |

5 | On Membrane Hierarchy in P Systems - Ibarra - 2005 |

5 | Simulations of Photosynthesis by a K-subset Transforming System with Membranes - Nishida - 2002 |

4 |
Paun’s Systems in Modeling of Human Resource Management
- Bartosik
- 2004
(Show Context)
Citation Context ...mantics [13], and making use of the parallelism, in solving parsing problems in an efficient way [45]), management (again, mainly at the l evel of the formalism and the graphical language, see, e.g., =-=[11]-=-, [12]), in devising sortin g and ranking algorithms [7], handling 2D structures [29], etc. In turn, the applications in biology follow in most cases a scenario of the following type: one examines a p... |