Elsevier

Theoretical Computer Science

Volume 623, 11 April 2016, Pages 65-74
Theoretical Computer Science

Small (purely) catalytic P systems simulating register machines

https://doi.org/10.1016/j.tcs.2015.09.020Get rights and content
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Abstract

The paper contributes to the topic of (purely) catalytic P systems. Catalytic P systems represent the original and likely the simplest class of membrane computing models. It is known that (purely) catalytic P systems with two (respectively three) catalysts and one membrane can simulate any Minsky register machine and, hence, they are computationally complete. However, the problem of minimal size of such a universal catalytic P system remains open for about ten years. We improve known results about small catalytic P systems simulating register machines in three different modes (generating, accepting, computing functions). Together with some specific universal register machine [7], one could eventually construct a small universal catalytic P system. As a consequence, we also improve the previous construction of a minimal catalytic P system generating a non-semilinear set, diminishing the number of necessary rules from 29 to 24.

Keywords

Membrane computing
Catalytic P system
Universal computation
Register machine

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