In this paper, we present a novel computing model, called probe machine (PM). Unlike the turing machine (TM), PM is a fully parallel computing model in the sense that it can simultaneously process multiple pairs of data, rather than sequentially process every pair of linearly adjacent data. We establish the mathematical model of PM as a nine-tuple consisting of data library, probe library, data controller, probe controller, probe operation, computing platform, detector, true solution storage, and residue collector. We analyze the computation capability of the PM model, and in particular, we show that TM is a special case of PM. We revisit two NP-complete problems, i.e., the graph coloring and Hamilton cycle problems, and devise two algorithms on basis of the established PM model, which can enumerate all solutions to each of these problems by only one probe operation. Furthermore, we show that PM can be implemented by leveraging the nano-DNA probe technologies. The computational power of an electronic computer based on TM is known far more than that of the human brain. A question naturally arises: will a future computer based on PM outperform the human brain in more ways beyond the computational power?

The solution space exponential explosion caused by the enumeration of the candidate solutions maybe is the biggest obstacle in DNA computing. In the paper, a new unenumerative DNA computing model for graph vertex coloring problem is presented based on two techniques: 1) ordering the vertex sequence for a given graph in such a way that any two consecutive labeled vertices i and i+1 should be adjacent in the graph as much as possible; 2) reducing the number of encodings representing colors according to the construture of the given graph. A graph with 12 vertices without triangles is solved and its initial solution space includes only 283 DNA strands, which is 0.0532 of 3¹² (the worst complexity).

In this paper, a logic computing model was constructed using a DNA nanoparticle, combined with color change technology of DNA/Au nanoparticle conjugates, and DNA computing. Several important technologies are utilized in this molecular computing model: DNA self-assembly, DNA/Au nanoparticle conjugation, and the color change resulting from Au nanoparticle aggregation. The simple logic computing model was realized by a color change, resulting from changing of DNA self-assembly. Based on this computing model, a set of operations computing model was also established, by which a simple logic problem was solved. To enlarge the applications of this logic nanocomputing system, a molecular detection method was developed for H1N1 virus gene detection.

DNA computing is an emerging computational model that has garnered significant attention due to its distinctive advantages at the molecular biological level. Since it was introduced by Adelman in 1994, this field has made remarkable progress in solving NP-complete problems, enhancing information security, encrypting images, controlling diseases, and advancing nanotechnology. A key challenge in DNA computing is the design of DNA coding, which aims to minimize nonspecific hybridization and enhance computational reliability. The DNA coding design is a classical combinatorial optimization problem focused on generating high-quality DNA sequences that meet specific constraints, including distance, thermodynamics, secondary structure, and sequence requirements. This paper comprehensively examines the advances in DNA coding design, highlighting mathematical models, counting theory, and commonly used DNA coding methods. These methods include the template method, multi-objective evolutionary methods, and implicit enumeration techniques.