2010 **Abstract:** Summary. 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 co…

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“…In [42], it was shown that a deterministic Turing machine working 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, using only communication rules.…”

confidence: 99%

“…In [42], it was shown that a deterministic Turing machine working 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, using only communication rules.…”

confidence: 99%

“…Several Turing machine simulations by means of polynomial-time uniform families of P systems have been proposed in the literature; some of these apply to unrestricted Turing machines [26,2], while others are limited to machines working in logarithmic space [25], polynomial time [7,6], polynomial space [32,24,17,10,12,13,15,16,14], or exponential space [1]. Most of these solutions [32,24,1,2,7,17,10,12,13,15,6,16,14] are able to simulate Turing machines working in polynomial time with a polynomial slowdown.…”

confidence: 99%

“…Known results of AM systems with polarizations reported in [3,22,44,46,47,62,66] are summarized in Table 1, with respect to various types of (dis)allowed rules the P system can use. Each column in the table defines a specific combination of allowed types of rules, and the last row displays the resulting class of problems solvable by uniform families of AM systems using only these kinds of rules.…”

confidence: 99%