We show that a deterministic single-tape Turing machine, operating in polynomial space with respect to the input length, can be efficiently simulated (both in terms of time and space) by a semi-uniform family of P systems with active membranes and three polarizations, using only communication rules. Then, basing upon this simulation, we prove that a result similar to the space hierarchy theorem can be obtained for P systems with active membranes: the larger the amount of space we can use during the computations, the harder the problems we are able to solve. © 2010 Springer-Verlag.
Valsecchi, A., Porreca, A., Leporati, A., Mauri, G., Zandron, C. (2010). An Efficient Simulation of Polynomial-Space Turing Machines by P Systems with Active Membranes. In Membrane Computing, 10th International Workshop, WMC10, Revised Selected and Invited Papers (pp.461-478). Springer-Verlag [10.1007/978-3-642-11467-0_31].
An Efficient Simulation of Polynomial-Space Turing Machines by P Systems with Active Membranes
VALSECCHI, ANDREA;PORRECA, ANTONIO ENRICO;LEPORATI, ALBERTO OTTAVIO;MAURI, GIANCARLO;ZANDRON, CLAUDIO
2010
Abstract
We show that a deterministic single-tape Turing machine, operating in polynomial space with respect to the input length, can be efficiently simulated (both in terms of time and space) by a semi-uniform family of P systems with active membranes and three polarizations, using only communication rules. Then, basing upon this simulation, we prove that a result similar to the space hierarchy theorem can be obtained for P systems with active membranes: the larger the amount of space we can use during the computations, the harder the problems we are able to solve. © 2010 Springer-Verlag.
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