P systems with active membranes: trading time for space

We consider recognizer P systems having three polarizations associated to the membranes, and we show that they are able to solve the PSPACEcomplete problem Quantified 3SAT when working in polynomial space and exponential time. The solution is uniform (all the instances of a fixed size are solved by the same P system) and uses only communication rules: evolution rules, as well as membrane division and dissolution rules, are not used. Our result shows that, as it happens with Turing machines, this model of P systems can solve in exponential time and polynomial space problems that cannot be solved in polynomial time, unless P = PSPACE.

• Type: Journal
• Year: 2011
• Where: NC
• Authors: Antonio E. Porreca, Alberto Leporati, Giancarlo Mauri, Claudio Zandron
• Keywords: Exponential Time, NC 2011, Neural Networks, Polynomial Space, Polynomial Space Problems