Int J Performability Eng ›› 2019, Vol. 15 ›› Issue (10): 2709-2717.doi: 10.23940/ijpe.19.10.p17.27092717

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Comparing Minimal Failure-Causing Schema and Probabilistic Failure-Causing Schema on Boolean Specifications

Ziyuan Wangab*, Xueyao Lia, Yang Lia, and Yuqing Daic   

  1. aSchool of Computer Science and Technology, Nanjing University of Posts and Telecommunications, Nanjing, 210023, China
    bTongda College, Nanjing University of Posts and Telecommunications, Yangzhou, 225127, China
    c School of Information Technology, Nanjing University of Chinese Medicine, Nanjing, 210023, China
  • Submitted on ; Revised on ; Accepted on
  • Contact: Wang Ziyuan
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    * Corresponding author. E-mail address:

  • Supported by:
    This work is supported by the National Nature Science Foundation of China (No 61772259) and the Foundation of Nanjing University of Posts and Telecommunications (No NY219079)


Both the model of minimal failure-causing schema (MFS) and the model of probabilistic failure-causing schema (PFS) were proposed to describe characteristics of failure test cases in input-domain testing. To improve the efficiency of software debugging, input variables that are related to failure-causing schemas should be closer to the real fault-relevant input variables. In order to examine which model (MFS or PFS) can help software engineers localize fault-relevant input variables more preciously, we conduct an experiment on general-form Boolean specifications extracted from the well-known TCAS system. For each mutant of a general-form Boolean expression, the set of input variables localized by the MFSs, the set of input variables localized by the PFSs, and the set of actual input variables involved in the fault are compared. Experimental results suggest that the MFS model usually has an advantage in terms of recall, while the PFS model usually has an advantage in terms of precision. Overall, the latter has a slight advantage in terms of f-measure.

Key words: input-domain testing, combinatorial testing, minimal failure-causing schema, probabilistic failure-causing schema, fault localization