1. Small (purely) catalytic P systems simulating register machines.
- Author
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Sosík, Petr and Langer, Miroslav
- Subjects
- *
SIMULATION methods & models , *BIOLOGICALLY inspired computing , *COMPUTATIONAL complexity , *MATHEMATICAL analysis , *COMPUTER science , *COMPUTER systems - 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. [ABSTRACT FROM AUTHOR]
- Published
- 2016
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