Solving PP-Complete and #P-Complete Problems by P Systems with Active Membranes

Authors:
Artiom Alhazov;Liudmila Burtseva;Svetlana Cojocaru;Yurii Rogozhin
Affiliations:
Institute of Mathematics and Computer Science, Academy of Sciences of Moldova, Chişinău, Moldova MD-2028;Institute of Mathematics and Computer Science, Academy of Sciences of Moldova, Chişinău, Moldova MD-2028;Institute of Mathematics and Computer Science, Academy of Sciences of Moldova, Chişinău, Moldova MD-2028;Institute of Mathematics and Computer Science, Academy of Sciences of Moldova, Chişinău, Moldova MD-2028 and Research Group on Mathematical Linguistics, Rovira i Virgili University, Tarr ...
Venue:
Membrane Computing
Year:
2009

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Abstract

Membrane computing is a formal framework of distributed parallel multiset processing. Due to massive parallelism and exponential space some intractable computational problems can be solved by P systems with active membranes in a polynomial number of steps. In this paper we generalize this approach from decisional problems to the computational ones, by providing a solution of a #P-complete problem, namely to compute the permanent of a binary matrix. The implication of this result to the PP complexity class is discussed and compared to known results about NP ∪ co − NP.