@article {2480,
	title = {GPU-parallel Crowd Simulation with Vulkan},
	journal = {6th International Workshop on Modeling and Simulation of and by Parallel and Distributed Systems (MSPDS 2020)},
	year = {2021},
	pages = {In press},
	url = {http://hpcs2020.cisedu.info/4-program/processed-manuscripts},
	author = {Antonio Torres-Mor{\'\i}{\~n}igo and Miguel A. Mart{\'\i}nez-del-Amor and Fernando Sancho-Caparrini}
}
@article {720,
	title = {A simulation algorithm for multienvironment probabilistic P systems: A formal verification},
	journal = {International Journal of Foundations of Computer Science},
	volume = {22},
	year = {2011},
	pages = {107-118},
	publisher = {World Scientific},
	address = {London, U.K.},
	issn = {0129-0541},
	author = {Miguel A. Mart{\'\i}nez-del-Amor and Ignacio P{\'e}rez-Hurtado and Mario J. P{\'e}rez-Jim{\'e}nez and Agust{\'\i}n Riscos-N{\'u}{\~n}ez and Fernando Sancho-Caparrini}
}
@proceedings {225,
	title = {Fourth Brainstorming Week on Membrane Computing},
	journal = {Fourth Brainstorming Week on Membrane Computing},
	volume = {II},
	year = {2006},
	month = {30/01/2006},
	pages = {XII+278},
	publisher = {F{\'e}nix Editora},
	address = {Seville (Spain)},
	isbn = {84-611-0519-2},
	url = {http://www.gcn.us.es/4BWMC/4BWMC_proceedings.htm},
	author = {Carmen Graciani-D{\'\i}az and Gheorghe Paun and {\'A}lvaro Romero-Jim{\'e}nez and Fernando Sancho-Caparrini}
}
@article {238,
	title = {The Growth of Branching Structures with P Systems},
	journal = {Fourth Brainstorming Week on Membrane Computing },
	volume = {II},
	year = {2006},
	month = {30/01-3/02/2006},
	pages = {253-265},
	publisher = {F{\'e}nix Editora},
	address = {Seville (Spain)},
	isbn = {84-611-0519-2},
	author = {{\'A}lvaro Romero-Jim{\'e}nez and Miguel A. Guti{\'e}rrez-Naranjo and Mario J. P{\'e}rez-Jim{\'e}nez},
	editor = {Carmen Graciani-D{\'\i}az and Gheorghe Paun and {\'A}lvaro Romero-Jim{\'e}nez and Fernando Sancho-Caparrini}
}
@article {236,
	title = {2006 Reseacrh Topics in Membrane Computing},
	journal = {Fourth Brainstorming Week on Membrane Computing },
	volume = {II},
	year = {2006},
	month = {1/30/06-2/3/06},
	pages = {235-251},
	publisher = {F{\'e}nix Editora},
	address = {Sevilla, Espa{\~n}a},
	isbn = {84-611-0519-2},
	author = {Gheorghe Paun},
	editor = {Carmen Graciani-D{\'\i}az and Gheorghe Paun and {\'A}lvaro Romero-Jim{\'e}nez and Fernando Sancho-Caparrini}
}
@article {240,
	title = {Solving 3-COL with Tissue P Systems},
	journal = {Fourth Brainstorming Week on Membrane Computing },
	volume = {II},
	year = {2006},
	month = {1/30/06-2/3/06},
	pages = {17-29},
	publisher = {F{\'e}nix Editora},
	address = {Sevilla, Espa{\~n}a},
	isbn = {84-611-0519-2},
	author = {Daniel D{\'\i}az-Pernil and Miguel A. Guti{\'e}rrez-Naranjo and Mario J. P{\'e}rez-Jim{\'e}nez},
	editor = {Carmen Graciani-D{\'\i}az and Gheorghe Paun and {\'A}lvaro Romero-Jim{\'e}nez and Fernando Sancho-Caparrini}
}
@article {252,
	title = {An Approach to the degree of parallelism in P systems},
	journal = {Fourth Brainstorming Week on Membrane Computing },
	volume = {II},
	year = {2006},
	pages = {87-104},
	publisher = {F{\'e}nix Editora},
	address = {Sevilla, Espa{\~n}a},
	isbn = {84-611-0519-2},
	author = {Miguel A. Guti{\'e}rrez-Naranjo and Mario J. P{\'e}rez-Jim{\'e}nez and Agust{\'\i}n Riscos-N{\'u}{\~n}ez and Francisco J. Romero-Campero},
	editor = {Carmen Graciani-D{\'\i}az and Gheorghe Paun and {\'A}lvaro Romero-Jim{\'e}nez and Fernando Sancho-Caparrini}
}
@article {533,
	title = {Computationally Hard Problems Addressed Through P Systems},
	journal = {Applications of Membrane Computing},
	year = {2006},
	pages = {315-346},
	publisher = {Springer-Verlag Berlin Heidelberg},
	chapter = {12},
	address = {Germany},
	isbn = {978-3-540-25017-3},
	doi = {10.1007/3-540-29937-8_12},
	url = {http://dx.doi.org/10.1007/3-540-29937-8_12},
	author = {Mario J. P{\'e}rez-Jim{\'e}nez and {\'A}lvaro Romero-Jim{\'e}nez and Fernando Sancho-Caparrini},
	editor = {Gabriel Ciobanu and Gheorghe Paun and Mario J. P{\'e}rez-Jim{\'e}nez}
}
@article {530,
	title = {A Polynomial Complexity Class in P Systems Using Membrane Division},
	journal = {Journal of Automata, Languages and Combinatorics},
	volume = {11},
	year = {2006},
	pages = {423-434},
	publisher = {Fakult{\"a}t f{\"u}r Informatik, Otto.von-Guericke-Universit{\"a}t},
	address = {Magdeburg (Germany)},
	issn = {1430-189X},
	author = {Mario J. P{\'e}rez-Jim{\'e}nez and {\'A}lvaro Romero-Jim{\'e}nez and Fernando Sancho-Caparrini}
}
@article {164,
	title = {Approximating Non-discrete P Systems},
	journal = {Lecture Notes in Computer Science},
	volume = {3365},
	year = {2005},
	pages = {287-295},
	publisher = {Springer},
	address = {Amsterdam, The Netherlands},
	abstract = {The main goal of this paper is to propose some geometric approaches to the computations of non-discrete P systems. The behavior of this kind of P systems is similar to that of classic systems, with the difference that the contents of the membranes are represented by non-discrete multisets (the multiplicities can be non-integers) and, consequently, also the number of applications of a rule in a transition step can be non-integer.
},
	isbn = {978-3-540-25080-7},
	issn = {0302-9743},
	url = {http://www.springerlink.com/index/73M2EXYEGKDFRLWF.pdf},
	author = {Andr{\'e}s Cord{\'o}n-Franco and Fernando Sancho-Caparrini}
}
@article {535,
	title = {Automated reasoning systems and molecular computing},
	journal = {Recent Results in Natural Computing},
	year = {2005},
	publisher = {F{\'e}nix Editora},
	address = {Sevilla, Spain},
	abstract = {This work was intended as an attempt to show the possible advantages provided by bringing together two areas, automated reasoning systems and DNA computing. The former as theoretical and formal devices to study the correctness of a program. The latter as practical devices to handle DNA strands to solve classical hard problems using laboratory techniques. To illustrate this approximation we present how we have obtained in the PVS proof checker the correctness of a program in a sticker based model for DNA computation. This result required a previous work: the formalization of the elected model within the PVS language. Also, in order to deal with imperative programs, we have studied a formalization of the Floyd-Hoare logic in the same system, PVS.},
	url = {http://www.cs.us.es/~marper/investigacion/carmen-rsme.pdf},
	attachments = {http://www.gcn.us.es/biblio/modules/system/files/carmen-rsme.pdf},
	author = {Carmen Graciani-D{\'\i}az and Mario J. P{\'e}rez-Jim{\'e}nez},
	editor = {Mario J. P{\'e}rez-Jim{\'e}nez and {\'A}lvaro Romero-Jim{\'e}nez and Fernando Sancho-Caparrini}
}
@article {537,
	title = {Formal verification of programs in molecular models with random access memory},
	journal = {Recent results in Natural Computing},
	year = {2005},
	pages = {205-229},
	publisher = {F{\'e}nix Editora},
	address = {Sevilla, Spain},
	url = {http://www.cs.us.es/~marper/investigacion/recent-2.pdf},
	attachments = {http://www.gcn.us.es/biblio/modules/system/files/recent-2.pdf},
	author = {Mario J. P{\'e}rez-Jim{\'e}nez and Fernando Sancho-Caparrini},
	editor = {Mario J. P{\'e}rez-Jim{\'e}nez and {\'A}lvaro Romero-Jim{\'e}nez and Fernando Sancho-Caparrini}
}
@article {538,
	title = {Generating pairwise disjoint families through DNA computations},
	journal = {Recent Results in Natural Computing},
	year = {2005},
	pages = {231-246},
	publisher = {F{\'e}nix Editora},
	address = {Sevilla, Spain},
	url = {http://www.cs.us.es/~marper/investigacion/recent-1.pdf},
	attachments = {http://www.gcn.us.es/biblio/modules/system/files/recent-1.pdf},
	author = {Mario J. P{\'e}rez-Jim{\'e}nez and Fernando Sancho-Caparrini},
	editor = {Mario J. P{\'e}rez-Jim{\'e}nez and {\'A}lvaro Romero-Jim{\'e}nez and Fernando Sancho-Caparrini}
}
@article {536,
	title = {Membrane computing as production systems},
	journal = {Recent Results in Natural Computing},
	year = {2005},
	pages = {167-204},
	publisher = {F{\'e}nix Editora},
	address = {Sevilla, Spain},
	url = {http://www.cs.us.es/~marper/investigacion/recent-3.pdf},
	attachments = {http://www.gcn.us.es/biblio/modules/system/files/recent-3.pdf},
	author = {Mario J. P{\'e}rez-Jim{\'e}nez and Francisco J. Romero-Campero},
	editor = {Mario J. P{\'e}rez-Jim{\'e}nez and {\'A}lvaro Romero-Jim{\'e}nez and Fernando Sancho-Caparrini}
}
@article {202,
	title = {Recent Results in Natural Computing},
	year = {2005},
	note = {Mario J. P{\'e}rez-Jim{\'e}nez; {\'A}lvaro Romero-Jim{\'e}nez; Fernando Sancho-Caparrini (eds.)},
	pages = {311},
	publisher = {F{\'e}nix Editora},
	address = {Seville (Spain)},
	abstract = {In the second part of the 20th century, a great deal of effort was devoted to understanding how computations take place in nature, and to benefit from this understanding by getting more efficient algorithms or even new types of computers. 
Within the First Joint Meeting between the RSME and the AMS, held in Sevilla, from June 18 to June 21, 2004, a Special Session entitled Biomolecular Mathematics was organized by Fernando Guzm{\'a}n and Tom Head, from Binghamton University (USA), Carlos Mart{\'\i}n-Vide, from University Rovira i Virgili of Tarragona (Spain), and Mario J. P{\'e}rez Jim{\'e}nez, from University of Sevilla (Spain). 
To that Session were invited, as speakers, Alessandra Carbone (Institut des Hautes Etudes Scientifiques), Rudolf Freund (Technische Universitaet Wien), Tero Harju (University of Turku), Mike Holcombe (University of Sheffield), Gheorghe Paun (Institute of Mathematics of the Romanian Academy), and Rani Siromoney (Madra Christian College). Following the conference presentations by the invited researchers, four talks were given, with the session being closed by a discussion of Recent results in Natural Computing. The title of this volume is intended to reflect the spirit of the last act that took place in the Special Session of Biomolecular Mathematics. The main goal of the volume is to present recent results in such research areas as evolutionary computing, molecular computing, and membrane computing, all of which belong to the emerging area of of Natural Computing, which is concerned with both the computing taking place in Nature and the new methods of computing inspired by Nature. 
All participants in the above mentioned Session of the Joint Meeting were invited to collaborate in this volume, as well as other prominent researchers belonging to the field of Natural Computing that could not attend the Special Session. 
We have collected 13 papers by 20 authors in the present volume. We hope that the papers collected here contribute to deepen the study of several topics in Natural Computing, and to strengthen some of the emerging lines in this field. 
We would like to thank all the authors for their good attitude towards participating in the elaboration of this book, as well as for the quality of the papers presented. They are the responsible and true editors of this publication. We also thank all who have had to decline our invitation because of their busy research agendas. 

},
	isbn = {84-609-5864-2},
	url = {http://books.google.com/books/about/Recent_results_in_natural_computing.html?id=eKcaPQAACAAJ},
	author = {Mario J. P{\'e}rez-Jim{\'e}nez and {\'A}lvaro Romero-Jim{\'e}nez and Fernando Sancho-Caparrini}
}
@article {286,
	title = {A CLIPS simulator for recognizer P systems with active membranes},
	journal = {Second Brainstorming Week on Membrane Computing},
	year = {2004},
	month = {February 2-7},
	pages = {387-413},
	address = {Sevilla, Espa{\~n}a},
	isbn = {84-688-6101-4},
	attachments = {http://www.gcn.us.es/biblio/modules/system/files/A CLIPS Simulator for Recognizer P Systems with Active Membrane.pdf},
	author = {Mario J. P{\'e}rez-Jim{\'e}nez},
	editor = {Gheorghe Paun and Agust{\'\i}n Riscos-N{\'u}{\~n}ez and {\'A}lvaro Romero-Jim{\'e}nez and Fernando Sancho-Caparrini}
}
@article {277,
	title = {Looking for P truth},
	journal = {Second Brainstorming Week on Membrane Computing},
	year = {2004},
	month = {February 2-7},
	pages = {134-138},
	address = {Sevilla, Espa{\~n}a},
	isbn = {84-688-6101-4},
	attachments = {http://www.gcn.us.es/biblio/modules/system/files/Looking for P Truth.pdf},
	author = {Andr{\'e}s Cord{\'o}n-Franco and Miguel A. Guti{\'e}rrez-Naranjo and Mario J. P{\'e}rez-Jim{\'e}nez},
	editor = {Gheorghe Paun and Agust{\'\i}n Riscos-N{\'u}{\~n}ez and {\'A}lvaro Romero-Jim{\'e}nez and Fernando Sancho-Caparrini}
}
@article {272,
	title = {Tissue P systems with cell division},
	journal = {Second Brainstorming Week on Membrane Computing},
	year = {2004},
	month = {February 2-7},
	pages = {380-386},
	isbn = {84-688-6101-4},
	attachments = {http://www.gcn.us.es/biblio/modules/system/files/Tissue P systems with cell division.pdf},
	author = {Gheorghe Paun and Mario J. P{\'e}rez-Jim{\'e}nez and Agust{\'\i}n Riscos-N{\'u}{\~n}ez},
	editor = {Gheorghe Paun and Agust{\'\i}n Riscos-N{\'u}{\~n}ez and {\'A}lvaro Romero-Jim{\'e}nez and Fernando Sancho-Caparrini}
}
@article {270,
	title = {Weak metrics on configurations of a P system},
	journal = {Second Brainstorming Week on Membrane Computing},
	year = {2004},
	month = {February 2-7},
	pages = {139-151},
	address = {Sevilla, Espa{\~n}a},
	isbn = {84-688-6101-4},
	url = {http://www.cs.us.es/~marper/investigacion/metricas.pdf},
	attachments = {http://www.gcn.us.es/biblio/modules/system/files/weak metrics on configurations of a P system.pdf},
	author = {Andr{\'e}s Cord{\'o}n-Franco and Miguel A. Guti{\'e}rrez-Naranjo and Mario J. P{\'e}rez-Jim{\'e}nez and Agust{\'\i}n Riscos-N{\'u}{\~n}ez},
	editor = {Gheorghe Paun and Agust{\'\i}n Riscos-N{\'u}{\~n}ez and {\'A}lvaro Romero-Jim{\'e}nez and Fernando Sancho-Caparrini}
}
@article {80,
	title = {A Prolog simulator for deterministic P systems with active membranes},
	journal = {New Generation Computing},
	volume = {22},
	year = {2004},
	month = {08/2004},
	pages = {349-363   },
	address = {Tokyo, Jap{\'o}n},
	abstract = {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 eaeh 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. 


},
	keywords = {logic programming, Membrane computing, prolog, SAT-problem, simulation},
	issn = {0288-3635 },
	url = {http://portal.acm.org/citation.cfm?id=1044475},
	author = {Andr{\'e}s Cord{\'o}n-Franco and Miguel A. Guti{\'e}rrez-Naranjo and Mario J. P{\'e}rez-Jim{\'e}nez and Fernando Sancho-Caparrini}
}
@proceedings {226,
	title = {Second Brainstorming Week on Membrane Computing},
	journal = {Second Brainstorming Week on Membrane Computing},
	year = {2004},
	note = {Gheorghe Paun; Agust{\'\i}n Riscos-N{\'u}{\~n}ez; {\'A}lvaro Romero-Jim{\'e}nez; Fernando Sancho-Caparrini (eds.)},
	month = {02/02/2004},
	pages = {456},
	address = {Seville (Spain)},
	isbn = {84-688-6101-4},
	url = {http://www.gcn.us.es/2BWMC/Volumen.htm},
	author = {Gheorghe Paun and Agust{\'\i}n Riscos-N{\'u}{\~n}ez and {\'A}lvaro Romero-Jim{\'e}nez and Fernando Sancho-Caparrini}
}
@article {,
	title = {Implementing in Prolog an effective cellular solution for the knapsack problem},
	journal = {Lecture Notes in Computer Science},
	volume = {2933},
	year = {2004},
	pages = {140-152},
	publisher = {Springer},
	address = {Amsterdam, The Netherlands},
	abstract = {In this paper we present an implementation in Prolog of an effective solution to the Knapsack problem via a family of deterministic P systems with active membranes using 2-division.},
	isbn = {978-3-540-20895-2},
	issn = {0302-9743},
	doi = {10.1007/b95207},
	url = {http://www.springerlink.com/content/dr7fphkr7l0vcy2e/?p=1c67f331bf084a449d112eb8de331656\&pi=9},
	author = {Andr{\'e}s Cord{\'o}n-Franco and Miguel A. Guti{\'e}rrez-Naranjo and Mario J. P{\'e}rez-Jim{\'e}nez and Agust{\'\i}n Riscos-N{\'u}{\~n}ez and Fernando Sancho-Caparrini}
}
@article {99,
	title = {Modelos de computaci{\'o}n celular con membranas},
	journal = {Bolet{\'\i}n de la Sociedad Espa{\~n}ola de Matem{\'a}tica Aplicada},
	volume = {29},
	year = {2004},
	pages = {57-88 },
	address = {Salamanca (Spain)},
	issn = {1575-9822},
	url = {http://www.sema.org.es/ojs/index.php?journal=sema\&page=issue\&op=view\&path\%5B\%5D=18},
	author = {Mario J. P{\'e}rez-Jim{\'e}nez and {\'A}lvaro Romero-Jim{\'e}nez and Fernando Sancho-Caparrini}
}
@article {,
	title = {A Note on Complexity Measures for Probabilistic P Systems},
	journal = {Journal of Universal Computer Science},
	volume = {10},
	year = {2004},
	pages = {559-566},
	address = {Granz Austria},
	abstract = {In this paper we present a first approach to the definition of different entropy measures for probabilistic P systems in order to obtain some quantitative parameters showing how complex the evolution of a P system is. To this end, we define two possible measures, the first one to reflect the entropy of the P system considered as the state space of possible computations, and the second one to reflect the change of the P system as it evolves. 
},
	keywords = {Entropy, Natural computing, P systems},
	url = {http://www.jucs.org/jucs_10_5/a_note_on_complexity},
	attachments = {http://www.gcn.us.es/biblio/modules/system/files/A note on Complexity Measures....pdf},
	author = {Andr{\'e}s Cord{\'o}n-Franco and Fernando Sancho-Caparrini}
}
@article {,
	title = {On the Reachability Problem for P Systems With Symport/Antiport},
	journal = {Publicationes Mathematicae Debrecen},
	volume = {65},
	year = {2004},
	pages = {603-627},
	address = {Debrecen, Hungr{\'\i}a},
	issn = {0033-3883},
	author = {Gheorghe Paun and Mario J. P{\'e}rez-Jim{\'e}nez and Fernando Sancho-Caparrini}
}
@article {195,
	title = {The P Versus NP Problem Through Cellular Computing with Membranes},
	journal = {Lecture Notes in Computer Science},
	volume = {2950},
	year = {2004},
	pages = {338-352},
	publisher = {Springer},
	address = {Amsterdam, The Netherlands},
	abstract = {We study the P versus NP problem through membrane systems. Language accepting P systems are introduced as a framework allowing us to obtain a characterization of the relation by the polynomial time unsolvability of an NP{\textendash}complete problem by means of a P system.},
	isbn = {978-3-540-20781-8},
	issn = {0302-9743},
	doi = {10.1007/978-3-540-24635-0_26},
	url = {http://dx.doi.org/10.1007/978-3-540-24635-0_26},
	author = {Mario J. P{\'e}rez-Jim{\'e}nez and {\'A}lvaro Romero-Jim{\'e}nez and Fernando Sancho-Caparrini}
}
@article {298,
	title = {Computing a Partial Mapping by a P System: Design and Verification},
	journal = {First Brainstorming Week on Membrane Computing },
	year = {2003},
	month = {February 5-11},
	pages = {247-260},
	address = {Tarragona, Spain},
	attachments = {http://www.gcn.us.es/biblio/modules/system/files/Computing a Partial Mapping by a P system  Design and Verification.pdf},
	author = {Antonio J. P{\'e}rez-Jim{\'e}nez and Mario J. P{\'e}rez-Jim{\'e}nez and Fernando Sancho-Caparrini},
	editor = {Matteo Cavaliere and Carlos Mart{\'\i}n-Vide and Gheorghe Paun}
}
@article {296,
	title = {Formal verification of a transition P system generating the set {2^n+n^2+n:n>=1}},
	journal = {First Brainstorming Week on Membrane Computing},
	year = {2003},
	month = {February 5-11},
	pages = {261-269},
	address = {Tarragona, Espa{\~n}a},
	attachments = {http://www.gcn.us.es/biblio/modules/system/files/Formal Verification of a Transition P System Generating the Set ....pdf},
	author = {Antonio J. P{\'e}rez-Jim{\'e}nez and Mario J. P{\'e}rez-Jim{\'e}nez and Fernando Sancho-Caparrini},
	editor = {Matteo Cavaliere and Carlos Mart{\'\i}n-Vide and Gheorghe Paun}
}
@article {287,
	title = {Verification of non deterministic transition P systems solving SAT problem },
	journal = {First Brainstorming Week on Membrane Computing},
	year = {2003},
	month = {February 5-11},
	pages = {291-304},
	address = {Tarragona, Spain},
	attachments = {http://www.gcn.us.es/biblio/modules/system/files/Verification of Non Detrministic Transition P systems solving SAT problems.pdf},
	author = {Fernando Sancho-Caparrini and Mario J. P{\'e}rez-Jim{\'e}nez},
	editor = {Matteo Cavaliere and Carlos Mart{\'\i}n-Vide and Gheorghe Paun}
}
@article {301,
	title = {Complexity Classes in Cellular  Computing with Membranes},
	journal = {Brainstorming Week on Membrane Computing},
	year = {2003},
	month = {5-11/02/2003},
	pages = {270-278},
	address = {Tarragona (Spain)},
	author = {Mario J. P{\'e}rez-Jim{\'e}nez and {\'A}lvaro Romero-Jim{\'e}nez and Fernando Sancho-Caparrini},
	editor = {Matteo Cavaliere and Carlos Mart{\'\i}n-Vide and Gheorghe Paun}
}
@article {290,
	title = {Solving VALIDITY Problem by Active Membranes with Input},
	journal = {Brainstorming Week on Membrane Computing},
	year = {2003},
	month = {5-11/02/2003},
	pages = {279-290},
	address = {Tarragona (Spain)},
	author = {Mario J. P{\'e}rez-Jim{\'e}nez and {\'A}lvaro Romero-Jim{\'e}nez and Fernando Sancho-Caparrini},
	editor = {Matteo Cavaliere and Carlos Mart{\'\i}n-Vide and Gheorghe Paun}
}
@article {300,
	title = {Complexity Classes in Cellular Computing with Membranes},
	journal = {First Joint Meeting between the RSME and the AMS},
	year = {2003},
	month = {18-21/06/2003},
	pages = {4},
	address = {Seville (Spain)},
	abstract = {Given a class of recognizer membrane systems F, the complexity class PMC_F of all prob-
lems solvable in polynomial time by a family of P systems of type F is presented. This
complexity class is stable by polynomial time reduction, and offer a new way to attack the
P = NP conjecture, now inside the framework of the cellular computing with membranes.},
	author = {Mario J. P{\'e}rez-Jim{\'e}nez and {\'A}lvaro Romero-Jim{\'e}nez and Fernando Sancho-Caparrini}
}
@article {299,
	title = {Complexity Classes in Cellular Computing with Membranes},
	journal = {First Annual Meeting of the European Molecular Computing Consortium},
	year = {2003},
	month = {15-17/05/2003},
	pages = {18},
	address = {Turku (Finland)},
	author = {Mario J. P{\'e}rez-Jim{\'e}nez and {\'A}lvaro Romero-Jim{\'e}nez and Fernando Sancho-Caparrini}
}
@article {302,
	title = {A Polynomial Complexity Class in P Systems Using Membrane Division},
	journal = {Fifth International Workshop on Descriptional Complexity of Formal Systems},
	year = {2003},
	month = {12-14/07/2003},
	pages = {284-294},
	address = {Budapest (Hungary)},
	isbn = {963-311-356-3},
	author = {Mario J. P{\'e}rez-Jim{\'e}nez and {\'A}lvaro Romero-Jim{\'e}nez and Fernando Sancho-Caparrini},
	editor = {Erzsebet Csuhaj-Varj{\'u} and C. Kintala and D. Wotschke and Gy{\"o}rgy Vaszil}
}
@article {114,
	title = {Complexity classes in models of cellular computing with membranes},
	journal = {Natural Computing},
	volume = {2},
	year = {2003},
	pages = {265 - 285   },
	publisher = {Springer Verlag},
	address = {Amsterdam, Netherlands},
	abstract = {In this paper we introduce four complexity classes for cellular computing systems with membranes: the first and the second ones contain all decision problems solvable in polynomial time by a family of deterministic P systems, without and with an input membrane, respectively; the third and fourth classes contain all decision problems solvable in polynomial time by a family of non-deterministic P systems, without and with an input membrane, respectively. We illustrate the usefulness of these classes by solving two NP{\textendash}complete problems, namely HPP and SAT, in both variants of P systems.



},
	keywords = {Complexity Classes, Membrane computing, P systems},
	issn = {1567-7818 },
	doi = {10.1023/A:1025449224520},
	url = {http://dx.doi.org/10.1023/A:1025449224520},
	author = {Mario J. P{\'e}rez-Jim{\'e}nez and {\'A}lvaro Romero-Jim{\'e}nez and Fernando Sancho-Caparrini}
}
@article {547,
	title = {Decision P systems and the P/=NP conjecture},
	journal = {Lecture Notes in Computer Science},
	volume = {2597},
	year = {2003},
	pages = {388-399},
	publisher = {Springer},
	address = {Amsterdam, The Netherlands},
	abstract = {We introduce decision P systems,which are a class of P systems with symbol-objects and external output. The main result of the paper is the following:if there exists an NP-complete problem that cannot be solved in polynomial time,with respect to the input length,by a deterministic decision P system constructed in polynomial time,then P/=NP. From Zandron-Ferreti-Mauri{\textquoteright}s theorem it follows that if P/= NP,then no NP-complete problem can be solved in polynomial time, with respect to the input length,by a deterministic P system with active membranes but without membrane division,constructed in polynomial time from the input. Together,these results give a characterization of P/=NP in terms of deterministic P systems. },
	isbn = {978-3-540-00611-4},
	issn = {0302-9743},
	doi = {10.1007/3-540-36490-0_27},
	url = {http://dx.doi.org/10.1007/3-540-36490-0_27},
	author = {Mario J. P{\'e}rez-Jim{\'e}nez and {\'A}lvaro Romero-Jim{\'e}nez and Fernando Sancho-Caparrini}
}
@article {,
	title = {Hybrid Networks of Evolutionary Processors},
	journal = {Lecture Notes in Computer Science},
	volume = {2723},
	year = {2003},
	pages = {401-412},
	publisher = {Springer},
	address = {Amsterdam, The Netherlands},
	abstract = {A hybrid network of evolutionary processors consists of several processors which are placed in nodes of a virtual graph and can perform one simple operation only on the words existing in that node in accordance with some strategies. Then the words which can pass the output filter of each node navigate simultaneously through the network and enter those nodes whose input filter was passed. We prove that these networks with filters defined by simple random-context conditions, used as language generating devices, are able to generate all linear languages in a very efficient way, as well as non-context-free languages. Then, when using them as computing devices, we present two linear solutions of the Common Algorithmic Problem.
},
	isbn = {978-3-540-40602-0},
	issn = {0302-9743},
	url = {http://www.springerlink.com/content/3yt2w7kgp6h5ctkm/?p=2bf594953627437eb4eed4e04713f308\&pi=48},
	author = {Carlos Mart{\'\i}n-Vide and Victor Mitrana and Mario J. P{\'e}rez-Jim{\'e}nez and Fernando Sancho-Caparrini}
}
@article {,
	title = {M{\'a}quinas moleculares basadas en ADN},
	journal = {Colecci{\'o}n de Divulgaci{\'o}n Cient{\'\i}fica},
	volume = {2},
	year = {2003},
	pages = {255},
	publisher = {Secretariado de Publicaciones. Universidad de Sevilla },
	address = {Seville},
	abstract = {La Computaci{\'o}n Natural o Biocomputaci{\'o}n es una disciplina inspirada en el funcionamiento de los organismos vivos y tiene como objetivo fundamental la simulaci{\'o}n e implementaci{\'o}n de los procesos din{\'a}micos que se dan en la Naturaleza y que son susceptibles de ser considerados como procedimientos de c{\'a}lculo. 

La Computaci{\'o}n Biomolecular es la rama de la Computaci{\'o}n Natural que trata del procesamiento de la informaci{\'o}n codificada a trav{\'e}s de macromol{\'e}culas (como el ADN, el ARN o las prote{\'\i}nas). En 1994 esta computaci{\'o}n pasa de un plano te{\'o}rico (in info) a un plano experimental ( in vitro). Es el nacimiento de la computaci{\'o}n molecular basada en ADN. 

Este libro tiene como objetivo principal el estudio de ciertas m{\'a}quinas moleculares dise{\~n}adas en modelos no convencionales dentro del marco de la Computaci{\'o}n Natural, desde el punto de vista de la potencia computacional y de la capacidad para atacar la resolubilidad de problemas matem{\'a}ticos especialmente dif{\'\i}ciles. 

Para ello, se han elegido tres modelos de computaci{\'o}n molecular que poseen caracter{\'\i}sticas dispares y usan como sustrato f{\'\i}sico el ADN. Los dos primeros, el modelo no restringido de Adleman y el modelo d{\'e}bil de Amos, son modelos sin memoria ya que sus operaciones primitivas no alteran la estructura interna de las mol{\'e}culas. El tercer modelo objeto de estudio es el modelo sticker, que admite operaciones que alteran dicha estructura y, por tanto, puede usar las mol{\'e}culas a modo de unidades de memoria, susceptibles de ser modificadas en en tiempo de ejecuci{\'o}n. 

Este libro es el primer texto escrito en lengua castellana dedicado a la Computaci{\'o}n Molecular basada en ADN. Esperamos y confiamos que su contenido proporcione m{\'e}todos y t{\'e}cnicas que puedan ser de utilidad para estudios posteriores acerca de dichos modelos no convencionales, en particular para el an{\'a}lisis de la robustez de procedimientos complejos descritos en dichos modelos y para la mecanizaci{\'o}n de los procesos de verificaci{\'o}n de programas moleculares en sistemas de razonamiento autom{\'a}tico. },
	isbn = {84-472-0777-3},
	url = {http://www.cs.us.es/~marper/investigacion/libroadn1.html},
	author = {Mario J. P{\'e}rez-Jim{\'e}nez and Fernando Sancho-Caparrini}
}
@article {186,
	title = {A MzScheme implementation of Transition P systems},
	journal = {Lecture Notes in Computer Science},
	volume = {2597},
	year = {2003},
	pages = {58-73},
	publisher = {Springer},
	address = {Amsterdam, The Netherlands},
	abstract = {The main goal of this paper is to present the design of an MzScheme program that allows us to simulate the behavior of transition P systems. For that, a library of procedures have been developed that work in two stages. In the first one, the parsing/compiling stage, the input P system is checked, and if it is well defined, then it is represented by means of an internal grammar. In a second stage, the simulation, the computation tree associated to the P system is generated until a prefixed level.
},
	issn = {0302-9743},
	url = {http://www.springerlink.com/content/lpn1vt6lajchxh9t/?p=bb2b349cabc24d1490b7d20ceeaab60e\&pi=4},
	author = {Delia Balbont{\'\i}n-Noval and Mario J. P{\'e}rez-Jim{\'e}nez and Fernando Sancho-Caparrini}
}
@article {,
	title = {On the Reachability Problem for P System with Porters},
	journal = {10th International Conference on Automata and Formal Languages},
	year = {2002},
	month = {August 13-18},
	pages = {1-3},
	address = {Debrecen, Hungr{\'\i}a},
	attachments = {http://www.gcn.us.es/biblio/modules/system/files/On the Reachability Problem for P systems with Porters.pdf},
	author = {Gheorghe Paun and Mario J. P{\'e}rez-Jim{\'e}nez and Fernando Sancho-Caparrini}
}
@article {,
	title = {Molecular Computation Models in ACL2: A Simulation of Lipton{\textquoteright}s SAT Experiment in the  Adleman{\textquoteright}s Restricted Model},
	journal = {Third International Workshop on the ACL2 Theorem Prover and its Applications},
	year = {2002},
	month = {April 8-9},
	pages = {175-187},
	address = {Grenoble, Francia},
	attachments = {http://www.gcn.us.es/biblio/modules/system/files/Molecular Computation Models in  ACL2.pdf},
	author = {Francisco J. Mart{\'\i}n-Mateos and Mario J. P{\'e}rez-Jim{\'e}nez and Fernando Sancho-Caparrini}
}
@article {307,
	title = {Formalizaci{\'o}n computacional del experimento de Lipton sobre el problema SAT},
	journal = {Primer Congreso Espa{\~n}ol de Algoritmos Evolutivos y Bioinspirados},
	year = {2002},
	month = {6-8/02/2002},
	pages = {326-332},
	address = {M{\'e}rida (Spain)},
	isbn = {84-607-3913-9},
	author = {Mario J. P{\'e}rez-Jim{\'e}nez and Fernando Sancho-Caparrini and Carmen Graciani-D{\'\i}az and {\'A}lvaro Romero-Jim{\'e}nez}
}
@article {187,
	title = {Solving Knapsack Problems in a Sticker Based Model },
	journal = {Lecture Notes in Computer Science},
	volume = {2340},
	year = {2002},
	month = {01/2002},
	pages = {161-171},
	publisher = {Springer},
	address = {Amsterdam, The Netherlands},
	abstract = {Our main goal in this paper is to give molecular solutions for two NP-complete problems, namely Subset-sum and Knapsack, in a sticker based model for DNA computations. In order to achieve this, we have used a finite set sorting subroutine together with the description of a procedure to formally verify the designed programs through the labeling of test tubes using inductive techniques.
},
	issn = {0302-9743},
	url = {http://www.springerlink.com/content/qcylexduk2m2pgtp/?p=2fd9a1af78134532a6ef254a6c313bb1\&pi=14},
	author = {Mario J. P{\'e}rez-Jim{\'e}nez and Fernando Sancho-Caparrini}
}
@article {,
	title = {Computaci{\'o}n Celular con Membranas: Un Modelo no Convencional },
	year = {2002},
	pages = {II+107},
	publisher = {Editorial Kronos},
	address = {Sevilla, Espa{\~n}a},
	isbn = {84-86273-52-8},
	url = {http://www.cs.us.es/~marper/investigacion/librocelular1.html},
	author = {Mario J. P{\'e}rez-Jim{\'e}nez and Fernando Sancho-Caparrini}
}
@article {,
	title = {A Formalization of Transition P Systems},
	journal = {Fundamenta Informaticae},
	volume = {49},
	year = {2002},
	pages = {261-272},
	publisher = {IOS Press},
	address = {Warsaw, Poland},
	abstract = {In this paper we give a complete formalization of a new computability model of a distributed parallel type which is inspired by some basic features of living cells: transition P systems as they were given in [3], addressed with completely different techniques than in [1] and [2]. For this, we present a formal syntax and semantic of the transition P systems capturing the synchronized work of P systems, and the nondeterministic and maximally parallel manner in which the rules of these systems can be applied. 


},
	keywords = {Formal Verification, Natural computing, P system},
	issn = {0169-2968},
	url = {http://portal.acm.org/citation.cfm?id=1220112},
	author = {Mario J. P{\'e}rez-Jim{\'e}nez and Fernando Sancho-Caparrini}
}
@article {222,
	title = {Teor{\'\i}a de la Complejidad en Modelos de Computaci{\'o}n Celular con Membranas},
	year = {2002},
	note = {Mario J. P{\'e}rez-Jim{\'e}nez; {\'A}lvaro Romero-Jim{\'e}nez; Fernando Sancho-Caparrini (coautores)},
	pages = {II+118 pages},
	publisher = {Editorial KRONOS},
	address = {Seville (Spain)},
	isbn = {84-86273-57-9},
	url = {http://www.cs.us.es/~marper/investigacion/librocelular2.html},
	author = {Mario J. P{\'e}rez-Jim{\'e}nez and {\'A}lvaro Romero-Jim{\'e}nez and Fernando Sancho-Caparrini}
}
@article {,
	title = {Verifying a P system generating squares},
	journal = {Romanian Journal of Information Science and Technology},
	volume = {5},
	year = {2002},
	pages = {181-191},
	publisher = {EDITURA ACADEMIEI ROM{\^A}NE},
	address = {Bucure{\c s}ti, Rom{\^a}nia},
	keywords = {Formal Verification, Membrane computing, Natural computing},
	issn = {1453-8245},
	url = {http://www.cs.us.es/~marper/investigacion/resumen-cuadrados.pdf},
	author = {Mario J. P{\'e}rez-Jim{\'e}nez and Fernando Sancho-Caparrini}
}
@article {852,
	title = {Initial segments maximal Σₙ-definable sets in fragments of arithmetic},
	journal = {Joint Conference of the 5th Barcelona Logic Meeting and the 6th Kurt G{\"o}del Colloquium},
	volume = {IV},
	year = {2001},
	month = {16-19/07/1999},
	pages = {37-38},
	publisher = {Kurt G ̈del Society},
	address = {Barcelona (Spain)},
	author = {Carmen Graciani-D{\'\i}az and Mario J. P{\'e}rez-Jim{\'e}nez and {\'A}lvaro Romero-Jim{\'e}nez and Fernando Sancho-Caparrini}
}
@article {850,
	title = {Soluciones moleculares del problema SAT de la L{\'o}gica Proposicional},
	journal = {Primeras Jornadas sobre L{\'o}gica y Lenguaje},
	year = {2000},
	month = {29/11-1/12/2000},
	pages = {243-252},
	publisher = {Editorial KRONOS},
	address = {Seville (Spain)},
	isbn = {84-85101-57-X},
	author = {Mario J. P{\'e}rez-Jim{\'e}nez and Carmen Graciani-D{\'\i}az and {\'A}lvaro Romero-Jim{\'e}nez and Fernando Sancho-Caparrini},
	editor = {{\'A}ngel Nepomuceno and Jos{\'e} F. Quesada and Francisco J. Salguero}
}
@article {849,
	title = {NP-Completitud y Computaci{\'o}n ADN},
	journal = {Encuentro de Matem{\'a}ticos Andaluces},
	volume = {II},
	year = {2000},
	month = {13-17/11/2000},
	pages = {539-548},
	publisher = {Universidad de Sevilla. Secretariado de Publicaciones},
	address = {Seville (Spain)},
	isbn = {84-472-0290-9},
	author = {Carmen Graciani-D{\'\i}az and Mario J. P{\'e}rez-Jim{\'e}nez and {\'A}lvaro Romero-Jim{\'e}nez and Fernando Sancho-Caparrini},
	editor = {Emilio Briales-Morales and Alfonso Carriazo-Rubio and Tom{\'a}s Chac{\'o}n-Rebollo and Pedro  Real and {\'A}lvaro Romero-Jim{\'e}nez}
}
