Computational efficiency of dissolution rules in membrane systems

Abstract

Trading (in polynomial time) space for time in the framework of membrane systems is not sufficient to efficiently solve computationally hard problems. On the one hand, an exponential number of objects generated in polynomial time is not sufficient to solve NP-complete problems in polynomial time. On the other hand, when an exponential number of membranes is created and used as workspace, the situation is very different. Two operations in P systems (membrane division and membrane creation) capable of constructing an exponential number of membranes in linear time are studied in this paper. NP-complete problems can be solved in polynomial time using P systems with active membranes and with polarizations, but when electrical charges are not used, then dissolution rules turn out to be very important. We show that in the framework of P systems with active membranes but without polarizations and in the framework of P systems with membrane creation, dissolution rules play a crucial role from the computational efficiency point of view.

Uniformity is Weaker than Semi-Uniformity for Some Membrane Systems

“…We note that there is a previous P characterisation for both uniform and semiuniform families of active membrane systems without charges and dissolution [21]: the same systems as we use here, but under much more general uniformity conditions, namely polynomial time, or P, uniformity. In that work the authors are motivated by the relationship with classes above P and so it is sufficient in their work to use P uniformity.…”

Monodirectional P systems

“…Indeed, when working in polynomial time and using only outward-bound communication, the corresponding complexity class decreases from PSPACE to P NP , or from P #P to P NP when non-elementary division and dissolution rules are disallowed. It is interesting to notice that, unlike with other restrictions such as removing membrane division [10] or charges and dissolution [2], the resulting P systems are still more powerful than P (unless, of course, P = NP).…”

“…Indeed, if a copy of 1 0 appears when h is positive, then another copy has been sent out in the previous step by rule (2); rule (25) eliminates such duplicates. When the tape head of M moves back to the leftmost cell, the machine can resume its original behaviour, and the encoding of the configuration of M in the P system is now correct according to the description given at the beginning of this section.…”

Simulation of P Systems with Active Membranes on CUDA

“…Parallelism, communication, non-determinism, synchronization, dynamic architecture of the model, etc, are aspects of the theory, with biological, mathematical and computer science sources of inspiration [13].…”