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Introducing a Space Complexity Measure for P Systems

Antonio E. Porreca, Alberto Leporati, Giancarlo Mauri, Claudio Zandron
2009 International Journal of Computers Communications & Control  
We define space complexity classes in the framework of membrane computing, giving some initial results about their mutual relations and their connection with time complexity classes, and identifying some  ...  We first consider the class of P systems with active membranes which do not make use of membrane division rules, usually denoted by N AM.  ...  results for time complexity classes in the framework of P systems with active membranes.  ... 
doi:10.15837/ijccc.2009.3.2779 fatcat:xutk47k535fxzk4gzqkdo4slpy

Alternative space definitions for P systems with active membranes

Artiom Alhazov, Alberto Leporati, Luca Manzoni, Giancarlo Mauri, Claudio Zandron
2021 Journal of Membrane Computing  
A different approach can also be considered, having in mind an implementation of P systems in silico; in this case, the multiplicity of each object in each membrane can be stored using binary numbers,  ...  classes and with complexity classes defined in the framework of P systems considering the original definition of space.  ...  In the article, it was shown that recognizer P systems with active membranes using polynomial space characterize the complexity class PSPACE .  ... 
doi:10.1007/s41965-021-00074-2 fatcat:oqi2esvyibdbdmz37zun7ve7mu

Computational Complexity Aspects in Membrane Computing [chapter]

Giancarlo Mauri, Alberto Leporati, Antonio E. Porreca, Claudio Zandron
2010 Lecture Notes in Computer Science  
system in a given moment) and the classes PSPACE, EXP, and EXPSPACE.  ...  In particular, we focus our attention on the comparison among complexity classes for membrane systems with active membranes (where new membranes can be created by division of membranes which exist in the  ...  In [17] it was shown that, unless P = NP, a confluent P system working without using membrane division cannot solve an NP-complete problem in polynomial time.  ... 
doi:10.1007/978-3-642-13962-8_35 fatcat:gxbunsr56fcfxkp45v3briky3u

P systems attacking hard problems beyond NP: a survey

Petr Sosík
2019 Journal of Membrane Computing  
These include P systems with active membranes, P systems with proteins on membranes and tissue P systems, as well as P systems with symport/antiport and membrane division and, finally, spiking neural P  ...  In the field of membrane computing, a great attention is traditionally paid to the results demonstrating a theoretical possibility to solve NP-complete problems in polynomial time by means of various models  ...  Note the use of oracles and complexity classes of the form , containing languages recognizable by polynomial-time Turing machines with oracles for languages in .  ... 
doi:10.1007/s41965-019-00017-y fatcat:4rs3f37vufcwja6fehdwdbqiom

A Computational Complexity Theory in Membrane Computing [chapter]

Mario J. Pérez–Jiménez
2010 Lecture Notes in Computer Science  
Polynomial complexity classes associated with different models of cell-like and tissue-like membrane systems are defined and the most relevant results obtained so far are presented.  ...  In this paper, a computational complexity theory within the framework of Membrane Computing is introduced.  ...  [5] showing that QBF-SAT can be solved in a linear time and in a uniform way by a family of recognizer P systems with active membranes (without using dissolution rules) and using division rules for  ... 
doi:10.1007/978-3-642-11467-0_10 fatcat:dxlxbkw74rbkpprpfq5g2w3mra

Complexity classes for membrane systems

Antonio E. Porreca, Giancarlo Mauri, Claudio Zandron
2006 RAIRO - Theoretical Informatics and Applications  
In particular, we focus our attention on the comparison among complexity classes for membrane systems with active membranes (where new membranes can be created by division of existing membranes) and the  ...  We compare various computational complexity classes defined within the framework of membrane systems, a distributed parallel computing device which is inspired from the functioning of the cell, with usual  ...  This work has been supported by the Italian Ministry of University (MIUR), under project PRIN-04 "Systems Biology: modellazione, linguaggi e analisi (SYBILLA)".  ... 
doi:10.1051/ita:2006001 fatcat:s5dar4emivcfnfvfazqjrnfsxq

A Framework for Complexity Classes in Membrane Computing

Agustín Riscos-Núñez
2009 Electronical Notes in Theoretical Computer Science  
in this area -of course, special attention is paid to the study of complexity classes.  ...  The purpose of the present work is to give a general idea about the existing results and open problems concerning the study of complexity classes within the membrane computing framework.  ...  We denote by AM the class of recognizer P systems with active membranes using only binary division for elementary membranes.  ... 
doi:10.1016/j.entcs.2008.12.083 fatcat:xtfjvx5rkrdmffego3gjf4ybwi

P Systems with Active Membranes Working in Sublinear Space [chapter]

Claudio Zandron, Alberto Leporati, Luca Manzoni, Giancarlo Mauri, Antonio E. Porreca
2014 Lecture Notes in Computer Science  
P systems with active membranes are a variant of P systems where the membranes can be created during the computation by division of existing ones.  ...  Using this feature, one can create an exponential number of membranes in a polynomial time, and use them in parallel to solve computationally hard problems, such as problems in NP or even in PSPACE.  ...  Research on the space complexity of P systems with active membranes has shown that these devices, when using a polynomial amount of space, exactly characterize the complexity class PSPACE [10], [11] .  ... 
doi:10.1007/978-3-319-14370-5_3 fatcat:qgbhvojxzbgvdijnp7lglun6jq

Computational efficiency of dissolution rules in membrane systems

Miguel A. Gutiérrez-Naranjo, Mario J. Pérez-Jiménez, Agustín Riscos-Núñez, Francisco J. Romero-Campero
2006 International Journal of Computer Mathematics  
In the next section, some preliminary ideas about recognizer membrane systems and polynomial complexity classes are introduced.  ...  Two operations in P systems (membrane division and membrane creation) capable of constructing an exponential number of membranes in linear time are studied in this paper.  ...  Acknowledgements The authors wish to acknowledge the support of the project TIN2005-09345-C04-01 of the Ministerio de Educación y Ciencia of Spain, co-financed by FEDER funds, and by a FPU fellowship to  ... 
doi:10.1080/00207160601065413 fatcat:q6kfqk5buvbcrlpnbgbloyvqam

Non-confluence in divisionless P systems with active membranes

Antonio E. Porreca, Giancarlo Mauri, Claudio Zandron
2010 Theoretical Computer Science  
We describe a solution to the SAT problem via non-confluent P systems with active membranes, without using membrane division rules.  ...  Together, these results prove that the complexity class of problems solvable nonconfluently and in polynomial time by this kind of P system is exactly the class NP.  ...  Pérez Jiménez for commenting on our results and pointing out an error in a preliminary version of Algorithm 1.  ... 
doi:10.1016/j.tcs.2009.07.032 fatcat:we6tq4q6qzhc7nmyoeoz22pshy

Bounding the space in P systems with active membranes

Claudio Zandron
2020 Journal of Membrane Computing  
P systems with active membranes have been widely used to attack problems in or even in ; in general, an exponential amount of space is generated in polynomial time by dividing existing membranes.  ...  Natural questions arise in this framework, concerning the power of P systems when different bounds are considered for the use of the space resource.  ...  Acknowledgements I wish to thank anonymous reviewers for providing me with useful comments on a previous version of this paper.  ... 
doi:10.1007/s41965-020-00039-x fatcat:fqubrpzcvjdcplldbz7rhidagu

Minimal cooperation as a way to achieve the efficiency in cell-like membrane systems

David Orellana-Martín, Luis Valencia-Cabrera, Agustín Riscos-Núñez, Mario J. Pérez-Jiménez
2019 Journal of Membrane Computing  
In this paper, two types of such membrane systems will be considered: (a) polarizationless P systems with active membranes without dissolution rules when minimal cooperation is permitted in object evolution  ...  Specifically, assuming that P is not equal to NP, several frontiers of the efficiency are obtained in these two computing frameworks, in such manner that each borderline provides a tool to tackle the P  ...  Acknowledgements This work is supported by the research project TIN2017-89842-P, cofinanced by Ministerio de Economía, Industria y Competitividad (MINECO) of Spain, through the Agencia Estatal de Investigación  ... 
doi:10.1007/s41965-018-00004-9 dblp:journals/jmemcom/Orellana-Martin19a fatcat:pl4gx2e7k5bxzjugg7s2gz3ude

Monodirectional P systems

Alberto Leporati, Luca Manzoni, Giancarlo Mauri, Antonio E. Porreca, Claudio Zandron
2016 Natural Computing  
In particular, we analyse the behaviour of P systems with active membranes where communication only happens from a membrane towards its parent, and never in the opposite direction.  ...  We investigate the influence that the flow of information in membrane systems has on their computational complexity.  ...  Indeed, when working in polynomial time and using only outward-bound communication, the corresponding complexity class decreases from PSPACE to P NP , or from P #P to P NP when non-elementary division  ... 
doi:10.1007/s11047-016-9565-2 fatcat:w4f5knebgjcmnn2dzrf3mrjkku

Tissue P Systems Can be Simulated Efficiently with Counting Oracles [chapter]

Alberto Leporati, Luca Manzoni, Giancarlo Mauri, Antonio E. Porreca, Claudio Zandron
2015 Lecture Notes in Computer Science  
This shows that the corresponding complexity classes are included in P #P , thus improving, under standard complexity theory assumptions, the previously known upper bound PSPACE.  ...  We prove that polynomial-time tissue P systems with cell division or cell separation can be simulated efficiently by Turing machines with oracles for counting problems.  ...  Conclusions We have proved a P #P upper bound to the class of problems solvable in polynomial time by uniform or semi-uniform families of tissue P systems using division or separation rules.  ... 
doi:10.1007/978-3-319-28475-0_17 fatcat:mqphjrdn25byviffttaftjklfm

Limits of the Power of Tissue P Systems with Cell Division [chapter]

Petr Sosík
2013 Lecture Notes in Computer Science  
Tissue P systems generalize the membrane structure tree usual in original models of P systems to an arbitrary graph.  ...  In this paper we show that computational power of these uniform families in polynomial time is limited by the class PSPACE.  ...  Acknowledgements This work was supported by the European Regional Development Fund in the IT4Innovations Centre of Excellence project (CZ.1.05/1.1.00/02.0070), and by the Silesian University in Opava under  ... 
doi:10.1007/978-3-642-36751-9_26 fatcat:azqmud2jonevncm6useimdocla
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