Computing with cells: membrane systems – some complexity issues

Membrane computing is a branch of natural computing which abstracts computing models from the structure and the functioning of the living cell. The main ingredients of membrane systems, called P systems, are (i) the membrane structure, which consists of a hierarchical arrangements of membranes which delimit compartments where (ii) multisets of symbols, called objects, evolve according to (iii) sets of rules which are localised and associated with compartments. By using the rules in a nondeterministic/deterministic maximally parallel manner, transitions between the system configurations can be obtained. A sequence of transitions is a computation of how the system is evolving. Various ways of controlling the transfer of objects from one membrane to another and applying the rules, as well as possibilities to dissolve, divide or create membranes have been studied. Membrane systems have a great potential for implementing massively concurrent systems in an efficient way that would allow us to solve currently intractable problems once future biotechnology gives way to a practical bio-realization. In this paper we survey some interesting and fundamental complexity issues such as universality vs. nonuniversality, determinism vs. nondeterminism, membrane and alphabet size hierarchies, characterizations of context-sensitive languages and other language classes and various notions of parallelism.

[1]  Gheorghe Paun,et al.  Spike Trains in Spiking Neural P Systems , 2006, Int. J. Found. Comput. Sci..

[2]  Gabriel Ciobanu,et al.  P Systems Running on a Cluster of Computers , 2003, Workshop on Membrane Computing.

[3]  Gheorghe Paun,et al.  Computing with Membranes: An Introduction , 1999, Bull. EATCS.

[4]  KariLila,et al.  Computationally universal P systems without priorities , 2005 .

[5]  Giancarlo Mauri,et al.  Solving NP-Complete Problems Using P Systems with Active Membranes , 2000, UMC.

[6]  L. Cardelli,et al.  Interactions of Biological Membranes , 2005 .

[7]  Andrei Paun,et al.  The power of communication: P systems with symport/antiport , 2002, New Generation Computing.

[8]  Oscar H. Ibarra,et al.  Characterizations of context-sensitive languages and other language classes in terms of symport/antiport P systems , 2006, Theor. Comput. Sci..

[9]  Artiom Alhazov,et al.  Symbol/Membrane Complexity of P Systems with Symport/Antiport Rules , 2005, Workshop on Membrane Computing.

[10]  Andrei Păun,et al.  On membrane computing based on splicing , 2001, Where Mathematics, Computer Science, Linguistics and Biology Meet.

[11]  Walter J. Savitch,et al.  Relationships Between Nondeterministic and Deterministic Tape Complexities , 1970, J. Comput. Syst. Sci..

[12]  Walter J. Savitch.  A note on multihead automata and context-sensitive languages , 2004, Acta Informatica.

[13]  Tseren-Onolt Ishdorj.  Minimal Parallelism for Polarizationless P Systems , 2006, DNA.

[14]  Luca Cardelli,et al.  Brane Calculi , 2004, CMSB.

[15]  Oscar H. Ibarra,et al.  Normal forms for spiking neural P systems , 2007, Theor. Comput. Sci..

[16]  Róbert Szelepcsényi,et al.  The method of forced enumeration for nondeterministic automata , 1988, Acta Informatica.

[17]  Oscar H. Ibarra,et al.  On various notions of parallelism in P Systems , 2005, Int. J. Found. Comput. Sci..

[18]  Andrei Paun,et al.  P Systems with Proteins on Membranes , 2006, Fundam. Informaticae.

[19]  Oscar H. Ibarra,et al.  On Deterministic Catalytic Systems , 2005, CIAA.

[20]  Mario de Jesús Pérez Jiménez,et al.  Cellular Computing (Complexity Aspects) , 2005 .

[21]  Gheorghe Paun.  P Systems with Active Membranes: Attacking NP-Complete Problems , 2001, J. Autom. Lang. Comb..

[22]  Oscar H. Ibarra.  Some Computational Issues in Membrane Computing , 2005, MFCS.

[23]  Rudolf Freund,et al.  Membrane Systems with Symport/Antiport Rules: Universality Results , 2002, WMC-CdeA.

[24]  Oscar H. Ibarra,et al.  On the Computational Power of 1-Deterministic and Sequential P Systems , 2006, Fundam. Informaticae.

[25]  Alfonso Rodríguez-Patón,et al.  Membrane computing and complexity theory: A characterization of PSPACE , 2007, J. Comput. Syst. Sci..

[26]  Rudolf Freund,et al.  Asynchronous P Systems and P Systems Working in the Sequential Mode , 2004, Workshop on Membrane Computing.

[27]  Christof Teuscher,et al.  A Hardware Membrane System , 2003 .

[28]  Oscar H. Ibarra,et al.  On the Computational Complexity of P Automata , 2004, DNA.

[29]  Rudolf Freund,et al.  Computationally universal P systems without priorities: two catalysts are sufficient , 2005, Theor. Comput. Sci..

[30]  Artiom Alhazov,et al.  Computational Power of Symport/Antiport: History, Advances, and Open Problems , 2005, Workshop on Membrane Computing.

[31]  Oscar H. Ibarra,et al.  Simulating FAS-induced apoptosis by using P systems , 2007 .

[32]  Mario J. Pérez-Jiménez,et al.  P Systems, a New Computational Modelling Tool for Systems Biology , 2006, Trans. Comp. Sys. Biology.

[33]  Gheorghe Păun.  Introduction: Membrane Computing — What It Is and What It Is Not , 2002 .

[34]  Mario J. Pérez-Jiménez,et al.  A Study of the Robustness of the EGFR Signalling Cascade Using Continuous Membrane Systems , 2005, IWINAC.

[35]  Gheorghe Paun,et al.  Computing with Membranes , 2000, J. Comput. Syst. Sci..

[36]  Florent Jacquemard,et al.  An Analysis of a Public Key Protocol with Membranes , 2005 .

[37]  Neil Immerman.  Nondeterministic Space is Closed Under Complementation , 1988, SIAM J. Comput..

[38]  Andrei Paun,et al.  P Systems with Proteins on Membranes and Membrane Division , 2006, Developments in Language Theory.

[39]  Gabriel Ciobanu,et al.  Applications of Membrane Computing , 2006, Applications of Membrane Computing.

[40]  Oscar H. Ibarra,et al.  On Bounded Symport/Antiport P Systems , 2005, DNA.

[41]  Gabriel Ciobanu,et al.  P systems with minimal parallelism , 2007, Theor. Comput. Sci..

[42]  Oscar H. Ibarra,et al.  On spiking neural P systems , 2006, Natural Computing.