## Solving vertex cover problem using DNA tile assembly model.(English)Zbl 1397.68075

Summary: DNA tile assembly models are a class of mathematically distributed and parallel biocomputing models in DNA tiles. In previous works, tile assembly models have been proved be Turing-universal; that is, the system can do what Turing machine can do. In this paper, we use tile systems to solve computational hard problem. Mathematically, we construct three tile subsystems, which can be combined together to solve vertex cover problem. As a result, each of the proposed tile subsystems consists of $$\Theta(1)$$ types of tiles, and the assembly process is executed in a parallel way (like DNA’s biological function in cells); thus the systems can generate the solution of the problem in linear time with respect to the size of the graph.

### MSC:

 68Q05 Models of computation (Turing machines, etc.) (MSC2010) 05C70 Edge subsets with special properties (factorization, matching, partitioning, covering and packing, etc.) 68Q10 Modes of computation (nondeterministic, parallel, interactive, probabilistic, etc.)
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