First Steps Towards Linking Membrane Depth and the Polynomial Hierarchy

Active membrane systems without charges are an extremely interesting group of models to study from the computational complexity point of view. Forbidding the use of a single rule type yields dramatic differences in computing power of these models. For example, it is known that systems with strong non-elementary division characterise PSPACE [1, 14], but when dissolution is forbidden these systems can solve at most problems in NL in the AC-semi-uniform case [7], and at most AC in the AC-uniform case [8]. Since AC ( NL ( PSPACE it seems these rules somehow capture different aspects of computation. In this report we present our first step towards a better understanding of the difference between P and PSPACE in terms of membrane systems. We suspect that the depth of a membrane system combined with non-elementary division is the key to this difference. Non-elementary division an operation where a membrane divides and all child membranes (and their child membranes etc.) get copied. There are two varieties of non-elementary division, “strong” which is triggered by membranes, and “weak” which is triggered by objects. (The labels “weak” and “strong” have nothing to do with the power of these rules.) Elementary division is where division is only permitted on membranes that do not have child membranes, and can be thought of as non-elementary division on structure of depth of 0.

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