Solving HPP and SAT by P Systems with Active Membranes and Separation Rules

The P systems (or membrane systems) are a class of distributed parallel computing devices of a biochemical type, where membrane division is the frequently investigated way for obtaining an exponential working space in a linear time, and on this basis solving hard problems, typically NP-complete problems, in polynomial (often, linear) time. In this paper, using another way to obtain exponential working space – membrane separation, it was shown that Satisfiability Problem and Hamiltonian Path Problem can be deterministically solved in linear or polynomial time by a uniform family of P systems with separation rules, where separation rules are not changing labels, but polarizations are used. Some related open problems are mentioned.

[1]  Gheorghe Paun,et al.  Second Brainstorming Week on Membrane Computing , 2004, J. Univers. Comput. Sci..

[2]  David S. Johnson,et al.  Computers and Intractability: A Guide to the Theory of NP-Completeness , 1978 .

[3]  Artiom Alhazov,et al.  Solving a PSPACE-Complete Problem by Recognizing P Systems with Restricted Active Membranes , 2003, Fundam. Informaticae.

[4]  Arto Salomaa,et al.  Formal languages , 1973, Computer science classics.

[5]  Michael Randolph Garey,et al.  Johnson: "computers and intractability , 1979 .

[6]  Artiom Alhazov,et al.  Membrane Operations in P Systems with Active Membranes , 2004 .

[7]  Koert N. J. Burger,et al.  Greasing Membrane Fusion and Fission Machineries , 2000, Traffic.

[8]  Gheorghe Paun,et al.  Regulated Rewriting in Formal Language Theory , 1989 .

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

[10]  Artiom Alhazov,et al.  Trading polarizations for labels in P systems with active membranes , 2004, Acta Informatica.

[11]  Artiom Alhazov,et al.  Further remarks on P systems with active membranes, separation, merging, and release rules , 2005, Soft Comput..

[12]  Mario J. Pérez-Jiménez,et al.  Complexity classes in models of cellular computing with membranes , 2003, Natural Computing.

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

[14]  John L. Casti,et al.  Unconventional Models of Computation , 2002, Lecture Notes in Computer Science.

[15]  Artiom Alhazov,et al.  Polarizationless P Systems with Active Membranes , 2004, Grammars.

[16]  David S. Johnson,et al.  Computers and In stractability: A Guide to the Theory of NP-Completeness. W. H Freeman, San Fran , 1979 .

[17]  Grzegorz Rozenberg,et al.  Handbook of Formal Languages , 1997, Springer Berlin Heidelberg.

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