Some Computational Issues in Membrane Computing

Membrane computing is a branch of molecular computing that aims to develop models and paradigms that are biologically motivated. It identifies an unconventional computing model, namely a P system, from natural phenomena of cell evolutions and chemical reactions. Because of the nature of maximal parallelism inherent in the model, P systems have a great potential for implementing massively concurrent systems in an efficient way that would allow us to solve currently intractable problems (in much the same way as the promise of quantum and DNA computing) once future bio-technology (or silicon-technology) gives way to a practical bio-realization (or chip realization). Here we report on recent results that answer some interesting and fundamental open questions in the field. These concern computational issues such as determinism versus nondeterminism, membrane and alphabet-size hierarchies, and various notions of parallelism.

[1]  Oscar H. Ibarra,et al.  On Model-Checking of P Systems , 2005, UC.

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

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

[4]  Rudolf Freund,et al.  P Systems without Priorities Are Computationally Universal , 2002, WMC-CdeA.

[5]  Alexandru T. Balaban,et al.  Mathematical Chemistry: (3, g)-Cages with Girth g, Topological Indices, and Other Graph-Theoretical Problems , 2004, Fundam. Informaticae.

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

[7]  Oscar H. Ibarra.  On membrane hierarchy in P systems , 2005, Theor. Comput. Sci..

[8]  Gheorghe Paun,et al.  Membrane Computing , 2002, Natural Computing Series.

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

[10]  Burkhard Monien.  Two-Way Multihead Automata Over a One-Letter Alphabet , 1980, RAIRO Theor. Informatics Appl..

[11]  Gheorghe Paun,et al.  A guide to membrane computing , 2002, Theor. Comput. Sci..

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

[13]  Oscar H. Ibarra,et al.  On Sequential and 1-Deterministic P Systems , 2005, COCOON.

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

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

[16]  Oscar H. Ibarra.  On determinism versus nondeterminism in P systems , 2005, Theor. Comput. Sci..

[17]  Oscar H. Ibarra,et al.  The Power of Maximal Parallelism in P Systems , 2004, Developments in Language Theory.

[18]  Gheorghe Paun,et al.  Symport/Antiport P Systems with Three Objects Are Universal , 2004, Fundam. Informaticae.

[19]  Pierluigi Frisco.  About P systems with symport/antiport , 2005, Soft Comput..

[20]  John E. Hopcroft,et al.  On the Reachability Problem for 5-Dimensional Vector Addition Systems , 1976, Theor. Comput. Sci..

[21]  Oscar H. Ibarra,et al.  Signaling P Systems and Verification Problems , 2005, ICALP.

[22]  Seymour Ginsburg,et al.  The mathematical theory of context free languages , 1966 .

[23]  Gheorghe Paun.  Further Twenty Six Open Problems in Membrane Computing , 2005 .

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

[25]  Sheila A. Greibach.  Remarks on Blind and Partially Blind One-Way Multicounter Machines , 1978, Theor. Comput. Sci..