Skip to main content
SpringerLink
Log in

The Complexity of Linear-Time Temporal Logic Model Repair

  • Conference paper
  • First Online:
Structured Object-Oriented Formal Language and Method (SOFL+MSVL 2017)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10795))

Abstract

We propose the model repair problem of the linear-time temporal logic. Informally, the repair problem asks for a minimum set of states in a given Kripke structure M, whose modification can make the given LTL formula satisfiable. We will examplify the application of the model and study the computational complexity of the problem. We will show the problem can be solved in exponential time but remains NP-hard even if k is a constant.

This is a preview of subscription content, log in via an institution to check access.

Access this chapter

Log in via an institution
Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD 39.99
Price excludes VAT (USA)
  • Available as EPUB and PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD 54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

References

  1. Balbiani, P., Jean-François, C.: Computational complexity of propositional linear temporal logics based on qualitative spatial or temporal reasoning. In: Armando, A. (ed.) FroCoS 2002. LNCS (LNAI), vol. 2309, pp. 162–176. Springer, Heidelberg (2002). https://doi.org/10.1007/3-540-45988-X_13

    Chapter  MATH  Google Scholar 

  2. Bauland, M., Schneider, T., Schnoor, H., Schnoor, I., Vollmer, H.: The complexity of generalized satisfiability for linear temporal logic. In: Seidl, H. (ed.) FoSSaCS 2007. LNCS, vol. 4423, pp. 48–62. Springer, Heidelberg (2007). https://doi.org/10.1007/978-3-540-71389-0_5

    Chapter  MATH  Google Scholar 

  3. Bruns, G., Godefroid, P.: Model checking partial state spaces with 3-valued temporal logics. In: Halbwachs, N., Peled, D. (eds.) CAV 1999. LNCS, vol. 1633, pp. 274–287. Springer, Heidelberg (1999). https://doi.org/10.1007/3-540-48683-6_25

    Chapter  Google Scholar 

  4. Buccafurri, F., Eiter, T., Gottlob, G., Leone, N.: Enhancing model checking in verification by AI techniques. Artif. Intell. 112(1), 57–104 (1999)

    Article  MathSciNet  Google Scholar 

  5. Chan, W.: Temporal-logic queries. In: Emerson, E.A., Sistla, A.P. (eds.) CAV 2000. LNCS, vol. 1855, pp. 450–463. Springer, Heidelberg (2000). https://doi.org/10.1007/10722167_34

    Chapter  Google Scholar 

  6. Clarke, E.M., Emerson, E.A.: Design and synthesis of synchronization skeletons using branching time temporal logic. In: Kozen, D. (ed.) Logic of Programs 1981. LNCS, vol. 131, pp. 52–71. Springer, Heidelberg (1982). https://doi.org/10.1007/BFb0025774

    Chapter  Google Scholar 

  7. Clarke, E., Grumberg, O., Jha, S., Lu, Y., Veith, H.: Counterexample-guided abstraction refinement. In: Emerson, E.A., Sistla, A.P. (eds.) CAV 2000. LNCS, vol. 1855, pp. 154–169. Springer, Heidelberg (2000). https://doi.org/10.1007/10722167_15

    Chapter  Google Scholar 

  8. Clarke, E.M., Grumberg, O., Peled, D.: Model Checking. MIT Press, London (1999)

    Google Scholar 

  9. Dasgupta, S., Papadimitriou, C.H., Vazirani, U.V.: Algorithms (2016)

    Google Scholar 

  10. Emerson, E.A., Halpern, J.Y.: Sometimes and not never revisited: on branching versus linear time temporal logic. J. ACM (JACM) 33(1), 151–178 (1986)

    Article  MathSciNet  Google Scholar 

  11. Finkbeiner, B., Torfah, H.: Counting models of linear-time temporal logic. In: Dediu, A.-H., Martín-Vide, C., Sierra-Rodríguez, J.-L., Truthe, B. (eds.) LATA 2014. LNCS, vol. 8370, pp. 360–371. Springer, Cham (2014). https://doi.org/10.1007/978-3-319-04921-2_29

    Chapter  Google Scholar 

  12. Gabbay, D., Pnueli, A., Shelah, S., Stavi, J.: On the temporal analysis of fairness. In: Proceedings of the 7th ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages, pp. 163–173. ACM (1980)

    Google Scholar 

  13. Groce, A., Chaki, S., Kroening, D., Strichman, O.: Error explanation with distance metrics. Int. J. Softw. Tools Technol. Transf. (STTT) 8(3), 229–247 (2006)

    Article  Google Scholar 

  14. Huth, M., Ryan, M.: Logic in Computer Science: Modelling and Reasoning About Systems. Cambridge University Press, Cambridge (2004)

    Book  Google Scholar 

  15. Lichtenstein, O., Pnueli, A.: Checking that finite state concurrent programs satisfy their linear specification. In: Proceedings of the 12th ACM SIGACT-SIGPLAN Symposium on Principles of Programming Languages, pp. 97–107. ACM (1985)

    Google Scholar 

  16. Mateis, C., Stumptner, M., Wotawa, F.: A value-based diagnosis model for Java programs (2000)

    Google Scholar 

  17. Pnueli, A.: The temporal logic of programs. In: 18th Annual Symposium on Foundations of Computer Science, pp. 46–57. IEEE (1977)

    Google Scholar 

  18. Reynolds, M.: The complexity of decision problems for linear temporal logics. J. Stud. Logic 3(1), 19–50 (2010)

    Google Scholar 

  19. Schnoebelen, P.: The complexity of temporal logic model checking. Adv. Modal Logic 4(393–436), 35 (2002)

    Google Scholar 

  20. Xiang, J., Machida, F., Tadano, K., Yanoo, K., Sun, W., Maeno, Y.: A static analysis of dynamic fault trees with priority-and gates. In: 2013 Sixth Latin-American Symposium on Dependable Computing (LADC), pp. 58–67. IEEE (2013)

    Google Scholar 

Download references

Acknowledgment

The support from the National Science Foundation of China (61772336, 61732013, 61472239) and the Key R&D Project of Zhejiang Province (2017C02036) is acknowledged.

Author information

Authors and Affiliations

  1. School of Software, Shanghai Jiao Tong University, Shanghai, China

    Xiuting Tao & Guoqiang Li

Authors
  1. Xiuting Tao
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Guoqiang Li
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Guoqiang Li .

Editor information

Editors and Affiliations

  1. Xidian University, Xi’an, China

    Cong Tian

  2. Nihon University, Tokyo, Japan

    Fumiko Nagoya

  3. Hosei University, Koganei-shi, Tokyo, Japan

    Shaoying Liu

  4. Xidian University, Xi’an, China

    Zhenhua Duan

Rights and permissions

Reprints and permissions

Copyright information

© 2018 Springer International Publishing AG, part of Springer Nature

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Tao, X., Li, G. (2018). The Complexity of Linear-Time Temporal Logic Model Repair. In: Tian, C., Nagoya, F., Liu, S., Duan, Z. (eds) Structured Object-Oriented Formal Language and Method. SOFL+MSVL 2017. Lecture Notes in Computer Science(), vol 10795. Springer, Cham. https://doi.org/10.1007/978-3-319-90104-6_5

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-90104-6_5

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-90103-9

  • Online ISBN: 978-3-319-90104-6

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation