Advertisement

An Efficient Approach for Computing Conflict Sets Combining Failure Probability with SAT

  • Ya Tao
  • Dantong Ouyang
  • Meng Liu
  • Liming Zhang
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11062)

Abstract

According to the topological structure of circuit and the characteristics of the enumeration tree, with the in-depth study of the reversed depth set enumeration tree method to compute conflict sets (CSRDSE), an efficient approach for counting conflict sets combining failure probability with SAT (CSCFPS) is proposed. Firstly, this paper presents the concept of fault output component set, possible fault component set, non-fault component set, explained fault component set, failure probability and non-conflict set theorem. Secondly, the OrderedCS-FP algorithm is came up. This algorithm calculates an ordered component set where the components are organized in descending order of failure probability. Finally, this paper puts forward the CSCFPS algorithm. In this algorithm, the SE-Tree is generated on the basis of the ordered component set, so minimal conflict set can be visited as early as possible to avoid the access to redundant nodes. On the grounds of the non-conflict set theorem, the sub-tree corresponding to the non-fault component set is deleted, decreasing the traversal to these nodes. Thus, the number of calling the SAT solver is greatly lessened. The experimental results show that the efficiency of this method is significantly improved.

Keywords

Model-based diagnosis Satisfiability (SAT) Set enumeration tree (SE-tree) Conflict set Failure probability 

Notes

Acknowledgements

This work was supported by the National Natural Science Foundation of China (61672261, 61502199, 61402196, 61373052).

References

  1. 1.
    Cai, S., Su, K.: Configuration checking with aspiration in local search for SAT. In: Proceedings of the Twenty-Sixth AAAI Conference on Artificial Intelligence, 22–26 July 2012, Toronto, Ontario, Canada, pp. 434–440 (2012)Google Scholar
  2. 2.
    Console, L., Dressler, O.: Model-based diagnosis in the real world: lessons learned and challenges remaining. In: Proceedings of the Sixteenth International Joint Conference on Artificial Intelligence, IJCAI 1999, Stockholm, Sweden, 31 July–6 August 1999, vols. 2, 1450 p., pp. 1393–1400 (1999)Google Scholar
  3. 3.
    Dai, S., Sun, H.: Computing conflict sets for model-based diagnosis. Control Theory Appl. 20(4), 630–632 (2003)Google Scholar
  4. 4.
    Fang, M.: A practical method to identify the minimal conflict sets. J. Hefei Univ. Technol. 22(1), 39–43 (1999)Google Scholar
  5. 5.
    Genesereth, M.R.: The use of design descriptions in automated diagnosis. Artif. Intell. 24(1–3), 411–436 (1984)CrossRefGoogle Scholar
  6. 6.
    Greiner, R., Smith, B.A., Wilkerson, R.W.: A correction to the algorithm in reiter’s theory of diagnosis. Artif. Intell. 41(1), 79–88 (1989)MathSciNetCrossRefGoogle Scholar
  7. 7.
    Haenni, R.: A query-driven anytime algorithm for argumentative and abductive reasoning. In: Bustard, D., Liu, W., Sterritt, R. (eds.) Soft-Ware 2002. LNCS, vol. 2311, pp. 114–127. Springer, Heidelberg (2002).  https://doi.org/10.1007/3-540-46019-5_9CrossRefGoogle Scholar
  8. 8.
    Hou, A.: A theory of measurement in diagnosis from first principles. Artif. Intell. 65(2), 281–328 (1994)MathSciNetCrossRefGoogle Scholar
  9. 9.
    Kleer, J.D.: An assumption-based TMS. Artif. Intell. 28(2), 127–162 (1986)CrossRefGoogle Scholar
  10. 10.
    Liu, M., Ouyang, D., Cai, S., Zhang, L.: Efficient zonal diagnosis with maximum satisfiability. Sci. China Inf. Sci. 61(11), 112101 (2018)CrossRefGoogle Scholar
  11. 11.
    Liu, M., Ouyang, D., Liu, B.: Grouped diagnosis approach using the feature of problem. Acta Electron. Sin. 46(3), 589–594 (2018)CrossRefGoogle Scholar
  12. 12.
    Luan, S., Dai, G.: Approach to diagnosing a system with structure information. Chin. J. Comput. 365, 178–189 (2005)Google Scholar
  13. 13.
    Nieuwenhuis, R., Oliveras, A., Tinelli, C.: Solving SAT and SAT modulo theories: from an abstract davis-putnam-logemann-loveland procedure to DPLL(T). J. ACM 53(6), 937–977 (2006)MathSciNetCrossRefGoogle Scholar
  14. 14.
    Ouyang, D., Liu, B., Zhou, J., Zhang, L.: A method of computing minimal conflict sets combining the structure property with the anti-depth SE-Tree. Acta Electron. Sin. 45(5), 1175–1181 (2017)Google Scholar
  15. 15.
    Reiter, R.: A theory of diagnosis from first principles. Artif. Intell. 32(1), 57–95 (1987)MathSciNetCrossRefGoogle Scholar
  16. 16.
    Wang, Y., Cai, S., Yin, M.: Two efficient local search algorithms for maximum weight clique problem. In: Proceedings of the Thirtieth AAAI Conference on Artificial Intelligence, 12–17 February 2016, Phoenix, Arizona, USA, pp. 805–811 (2016)Google Scholar
  17. 17.
    Wang, Y., Cai, S., Yin, M.: Local search for minimum weight dominating set with two-level configuration checking and frequency based scoring function. J. Artif. Intell. Res. 58, 267–295 (2017)MathSciNetCrossRefGoogle Scholar
  18. 18.
    Wang, Y., Cai, S., Yin, M.: New heuristic approaches for maximum balanced biclique problem. Inf. Sci. 432, 362–375 (2018)MathSciNetCrossRefGoogle Scholar
  19. 19.
    Wotawa, F.: A variant of reiter’s hitting-set algorithm. Inf. Process. Lett. 79(1), 45–51 (2001)MathSciNetCrossRefGoogle Scholar
  20. 20.
    Zhang, J., Ma, F., Zhang, Z.: Faulty interaction identification via constraint solving and optimization. In: Cimatti, A., Sebastiani, R. (eds.) SAT 2012. LNCS, vol. 7317, pp. 186–199. Springer, Heidelberg (2012).  https://doi.org/10.1007/978-3-642-31612-8_15CrossRefGoogle Scholar
  21. 21.
    Zhao, X., Ouyang, D.: A method of combining SE-tree to compute all minimal hitting sets. Progress Nat. Sci.: Mater. Int. 16(2), 169–174 (2006)MathSciNetCrossRefGoogle Scholar
  22. 22.
    Zhao, X., Ouyang, D.: Deriving all minimal conflict sets using satisfiability algorithms. Acta Electron. Sin. 37(4), 804–810 (2009)Google Scholar

Copyright information

© Springer Nature Switzerland AG 2018

Authors and Affiliations

  • Ya Tao
    • 1
    • 2
  • Dantong Ouyang
    • 1
    • 2
  • Meng Liu
    • 1
    • 2
  • Liming Zhang
    • 1
    • 2
  1. 1.Key Laboratory of Symbolic Computation and Knowledge Engineering of Ministry of EducationJilin UniversityChangchunChina
  2. 2.School of Computer Science and TechnologyJilin UniversityChangchunChina

Personalised recommendations