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Probe Machine Based Computing Model for Solving Satisfiability Problem

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Bio-inspired Computing: Theories and Applications (BIC-TA 2019)

Part of the book series: Communications in Computer and Information Science ((CCIS,volume 1160))

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Abstract

Probe Machine (PM) is a recently reported theoretical model with massive parallelism. Particularly, Turing Machine (TM) had been proven to be the special case of PM. The paper proposed a PM based computing model for satisfiability problem. PM is capable of searching pairs of data fiber that are complementary to pre-devised probes, leading to the connection of pairs of data in parallel. We encoded the assignment to variables in the given 3-SAT formula into data fibers and devised probes between pairs of data fiber, the unique satisfying assignment of a hard 3-SAT formula could be generated within just one step of probe operation. More generally, for an arbitrary 3-SAT formula with variables and clauses, we presented a method for deciding the satisfiability using the concept of potential probe. Complexity analysis shows the encoding complexity and time complexity of the proposed model are o(n) and o(1), respectively. The distinguishing characteristics of the proposed model lie in two aspects. On one hand, solution to NP-complete problem was generated in just one step of probe operation rather than found in vast solution space. On the other hand, the proposed model is highly parallel. Most important of all, the parallelism increases with problem size. This marks a giant step in computational theory. With the parallel search capability inherited in PM, the size of NP-complete search problems is expected to be increased further.

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Acknowledgments

The authors would like to thank every author appeared in the references. This work was supported by National Natural Science Foundation of China [61672001, 61702008], Natural Science Foundation of Anhui University [KJ2019A0538], and [18-163-ZT-005-009-01].

Author information

Authors and Affiliations

  1. School of Electronic and Information Engineering, Anhui University of Science and Technology, Huainan, 232001, Anhui, China

    Jianzhong Cui

  2. School of Mathematics, Physics and Statistics, Shanghai University of Engineering Science, Shanghai, 201620, People’s Republic of China

    Zhixiang Yin

  3. School of Mathematics and Big Data, Anhui University of Science and Technology, Huainan, 232001, Anhui, China

    Jing Yang & Xianya Geng

  4. Department of Computer, Huainan Union University, Huainan, 232038, Anhui, China

    Jianzhong Cui

  5. School of Computer Science, Dalian University of Technology, Dalian, 116024, Liaoning, China

    Qiang Zhang

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  1. Jianzhong Cui
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  3. Jing Yang
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  4. Xianya Geng
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  5. Qiang Zhang
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Corresponding author

Correspondence to Zhixiang Yin .

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Editors and Affiliations

  1. Huazhong University of Science and Technology, Wuhan, China

    Linqiang Pan

  2. Zhengzhou University, Zhengzhou, China

    Jing Liang

  3. Zhongyuan University of Technology, Zhengzhou, China

    Boyang Qu

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Cui, J., Yin, Z., Yang, J., Geng, X., Zhang, Q. (2020). Probe Machine Based Computing Model for Solving Satisfiability Problem. In: Pan, L., Liang, J., Qu, B. (eds) Bio-inspired Computing: Theories and Applications. BIC-TA 2019. Communications in Computer and Information Science, vol 1160. Springer, Singapore. https://doi.org/10.1007/978-981-15-3415-7_7

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  • DOI: https://doi.org/10.1007/978-981-15-3415-7_7

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  • Online ISBN: 978-981-15-3415-7

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