On the computational complexity of membrane systems

Oscar H. Ibarra
2004 Theoretical Computer Science  
We show how techniques in machine-based complexity can be used to analyze the complexity of membrane computing systems. We focus on catalytic systems, communicating P systems, and systems with only symport/antiport rules, but our techniques are applicable to other P systems that are universal. We deÿne space and time complexity measures and show hierarchies of complexity classes similar to well-known results concerning Turing machines and counter machines. We also show that the deterministic
more » ... municating P system simulating a deterministic counter machine in 264-275.) can be constructed to have a ÿxed number of membranes, answering positively an open question in Sosik (2002) , Sosik and Matysek (2002) . We prove that reachability of extended conÿgurations for symport/antiport systems (as well as for catalytic systems and communicating P systems) can be decided in nondeterministic log n space and, hence, in deterministic log 2 n space or in polynomial time, improving the main result in (On the reachability problem for P systems with symport/antiport, 2002, submitted for publication.). We propose two equivalent systems that deÿne languages (instead of multisets of objects): the ÿrst is a catalytic system language generator and the other is a communicating P system acceptor (or a symport/antiport system acceptor). These devices are universal and therefore can also be analyzed with respect to space and time complexity. Finally, we give a characterization of semilinear languages in terms of a restricted form of catalytic system language generator.
doi:10.1016/j.tcs.2004.03.045 fatcat:6gm6hnd2grb4tbo4v2r5ljs2xm