Skip to main content
Springer Nature Link
Log in

\(\textsc {Reach}\) on Register Automata via History Independence

  • Conference paper
  • First Online:
Tests and Proofs (TAP 2022)

Part of the book series: Lecture Notes in Computer Science ((LNCS,volume 13361))

Included in the following conference series:

  • 447 Accesses

Abstract

Register automata are an expressive model of computation using finite memory. Conformance checking of their properties can be reduced to \(\textsc {NonEmptiness}\) tests, however, this problem is \(\mathsf {PSPACE}\)-complete. Existing approaches usually employ symbolic state exploration. This results in state explosion for most complex register automata. We propose a semantics-preserving transformation of register automata into a representation in which reachability of states is equivalent to reachability of locations, i.e., is in \(\mathsf {NL}\). We evaluate the algorithm on random-generated and real-world automata and show that it avoids state explosion and performs better on most instances than a comparable existing approach. This yields a practical approach to conformance checking of register automata.

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

Access this chapter

Log in via an institution

Subscribe and save

Springer+ Basic
$34.99 /Month
  • Get 10 units per month
  • Download Article/Chapter or eBook
  • 1 Unit = 1 Article or 1 Chapter
  • Cancel anytime
Subscribe now

Buy Now

Chapter
USD 29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever

Tax calculation will be finalised at checkout

Purchases are for personal use only

Institutional subscriptions

Similar content being viewed by others

Notes

  1. 1.

    https://github.com/tudo-aqua/koral.

  2. 2.

    https://bitbucket.org/learnlib/ralib/src/eqmc.

  3. 3.

    https://github.com/tudo-aqua/jconstraints.

  4. 4.

    https://github.com/Z3Prover/z3.

  5. 5.

    https://automata.cs.ru.nl.

References

  1. Aarts, F., Heidarian, F., Kuppens, H., Olsen, P., Vaandrager, F.: Automata learning through counterexample guided abstraction refinement. In: Giannakopoulou, D., Méry, D. (eds.) FM 2012. LNCS, vol. 7436, pp. 10–27. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-32759-9_4

    Chapter  Google Scholar 

  2. Aarts, F., Jonsson, B., Uijen, J.: Generating models of infinite-state communication protocols using regular inference with abstraction. In: Petrenko, A., Simão, A., Maldonado, J.C. (eds.) ICTSS 2010. LNCS, vol. 6435, pp. 188–204. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-16573-3_14

    Chapter  Google Scholar 

  3. Aarts, F., Schmaltz, J., Vaandrager, F.: Inference and abstraction of the biometric passport. In: Margaria, T., Steffen, B. (eds.) ISoLA 2010. LNCS, vol. 6415, pp. 673–686. Springer, Heidelberg (2010). https://doi.org/10.1007/978-3-642-16558-0_54

    Chapter  Google Scholar 

  4. Bartlett, K.A., Scantlebury, R.A., Wilkinson, P.T.: A note on reliable full-duplex transmission over half-duplex links. Commun. ACM 12(5), 260–261 (1969). https://doi.org/10.1145/362946.362970

    Article  Google Scholar 

  5. Boigelot, B.: Symbolic methods for exploring infinite state spaces. Ph.D. thesis, Université de Liège, Liège, Belgium, May 1998. https://hdl.handle.net/2268/74874

  6. Bojańczyk, M., Klin, B., Lasota, S.: Automata theory in nominal sets. Log. Methods Comput. Sci. 10(4), 1–44 (2014). https://doi.org/10.2168/LMCS-10(3:4)2014

    Article  Google Scholar 

  7. Brütsch, B., Landwehr, P., Thomas, W.: \(\mathbb{N}\)-memory automata over the alphabet \(\mathbb{N}\). In: Drewes, F., Martín-Vide, C., Truthe, B. (eds.) LATA 2017. LNCS, vol. 10168, pp. 91–102. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-53733-7_6

    Chapter  Google Scholar 

  8. Cassel, S., Howar, F., Jonsson, B.: RALib: a LearnLib extension for inferring EFSMs. In: Proceedings of the 4th International Workshop on Design and Implementation of Formal Tools and Systems (2015). https://www.faculty.ece.vt.edu/chaowang/difts2015/papers/paper_5.pdf

  9. Cassel, S., Howar, F., Jonsson, B., Merten, M., Steffen, B.: A succinct canonical register automaton model. In: Bultan, T., Hsiung, P.-A. (eds.) ATVA 2011. LNCS, vol. 6996, pp. 366–380. Springer, Heidelberg (2011). https://doi.org/10.1007/978-3-642-24372-1_26

    Chapter  Google Scholar 

  10. Cassel, S., Jonsson, B., Howar, F., Steffen, B.: A succinct canonical register automaton model for data domains with binary relations. In: Chakraborty, S., Mukund, M. (eds.) ATVA 2012. LNCS, pp. 57–71. Springer, Heidelberg (2012). https://doi.org/10.1007/978-3-642-33386-6_6

    Chapter  Google Scholar 

  11. Chen, Y.F., Lengál, O., Tan, T., Wu, Z.: Register automata with linear arithmetic. In: 2017 32nd Annual ACM/IEEE Symposium on Logic in Computer Science (LICS), pp. 1–12. IEEE, June 2017. https://doi.org/10.1109/LICS.2017.8005111

  12. Cormen, T.H., Leiserson, C.E., Rivest, R.L., Stein, C.: All-Pairs Shortest Paths, chap. 25, 3rd edn. pp. 684–707. MIT Press, Cambridge, February 2009

    Google Scholar 

  13. Czyba, C., Spinrath, C., Thomas, W.: Finite automata over infinite alphabets: two models with transitions for local change. In: Potapov, I. (ed.) DLT 2015. LNCS, vol. 9168, pp. 203–214. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-21500-6_16

    Chapter  Google Scholar 

  14. D’Antoni, L., Ferreira, T., Sammartino, M., Silva, A.: Symbolic register automata. In: Dillig, I., Tasiran, S. (eds.) CAV 2019. LNCS, vol. 11561, pp. 3–21. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-25540-4_1

    Chapter  Google Scholar 

  15. Demri, S., Lazić, R.: LTL with the freeze quantifier and register automata. ACM Trans. Comput. Log. 10(3), 16:1–16:30 (2009). https://doi.org/10.1145/1507244.1507246

  16. Dierl, S., Howar, F.: A taxonomy and reductions for common register automata formalisms. In: Olderog, E.-R., Steffen, B., Yi, W. (eds.) Model Checking, Synthesis, and Learning. LNCS, vol. 13030, pp. 186–218. Springer, Cham (2021). https://doi.org/10.1007/978-3-030-91384-7_10

    Chapter  Google Scholar 

  17. Dierl, S., Howar, F.: Reach on register automata via history independence - replication artifact (2022). https://doi.org/10.5281/zenodo.6367981

  18. Garhewal, B., Vaandrager, F., Howar, F., Schrijvers, T., Lenaerts, T., Smits, R.: Grey-box learning of register automata. In: Dongol, B., Troubitsyna, E. (eds.) IFM 2020. LNCS, vol. 12546, pp. 22–40. Springer, Cham (2020). https://doi.org/10.1007/978-3-030-63461-2_2

    Chapter  Google Scholar 

  19. Granas, A., Dugundji, J.: Elementary fixed point theorems, chap. 2, pp. 9–84. Springer, New York (2003). https://doi.org/10.1007/978-0-387-21593-8_2

  20. Hoare, C.A.R.: An axiomatic basis for computer programming. Commun. ACM 12(10), 576–580 (1969). https://doi.org/10.1145/363235.363259

    Article  Google Scholar 

  21. Howar, F., Jabbour, F., Mues, M.: JConstraints: a library for working with logic expressions in java. In: Margaria, T., Graf, S., Larsen, K.G. (eds.) Models, Mindsets, Meta: The What, the How, and the Why Not? LNCS, vol. 11200, pp. 310–325. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-22348-9_19

    Chapter  Google Scholar 

  22. International Civil Aviation Organization: Machine readable travel documents. Doc 9303, International Civil Aviation Organization, Montréal, Québec, Canada (2021). https://www.icao.int/publications/pages/publication.aspx?docnum=9303

  23. Iosif, R., Xu, X.: Abstraction refinement for emptiness checking of alternating data automata. In: Beyer, D., Huisman, M. (eds.) TACAS 2018. LNCS, vol. 10806, pp. 93–111. Springer, Cham (2018). https://doi.org/10.1007/978-3-319-89963-3_6

    Chapter  Google Scholar 

  24. Kaminski, M., Francez, N.: Finite-memory automata. Theor. Comput. Sci. 134(2), 329–363 (1994). https://doi.org/10.1016/0304-3975(94)90242-9

    Article  Google Scholar 

  25. Madelaine, E., Qin, X., Zhang, M., Bliudze, S.: Using SMT engine to generate symbolic automata. Electron. Commun. EASST 76 (2019). https://doi.org/10.14279/tuj.eceasst.76.1103

  26. Minsky, M.L.: Computation: Finite and infinite machines. Prentice-Hall International, London (1972)

    Google Scholar 

  27. Moerman, J., Sammartino, M.: Residual nominal automata. In: Konnov, I., Kovács, L. (eds.) 31st International Conference on Concurrency Theory. LIPIcs, vol. 171, pp. 44:1–44:21. Schloss Dagstuhl-Leibniz-Zentrum für Informatik, Dagstuhl, Germany (2020). https://doi.org/10.4230/LIPIcs.CONCUR.2020.44

  28. de Moura, L., Bjørner, N.: Z3: an efficient SMT solver. In: Ramakrishnan, C.R., Rehof, J. (eds.) TACAS 2008. LNCS, vol. 4963, pp. 337–340. Springer, Heidelberg (2008). https://doi.org/10.1007/978-3-540-78800-3_24

    Chapter  Google Scholar 

  29. Murawski, A.S., Ramsay, S.J., Tzevelekos, N.: Reachability in pushdown register automata. In: Csuhaj-Varjú, E., Dietzfelbinger, M., Ésik, Z. (eds.) MFCS 2014. LNCS, vol. 8634, pp. 464–473. Springer, Heidelberg (2014). https://doi.org/10.1007/978-3-662-44522-8_39

    Chapter  Google Scholar 

  30. Murawski, A.S., Ramsay, S.J., Tzevelekos, N.: Reachability in pushdown register automata. J. Comput. Syst. Sci 87, 58–83 (2017). https://doi.org/10.1016/j.jcss.2017.02.008

    Article  Google Scholar 

  31. Neider, D., Smetsers, R., Vaandrager, F., Kuppens, H.: Benchmarks for automata learning and conformance testing. In: Margaria, T., Graf, S., Larsen, K.G. (eds.) Models, Mindsets, Meta: The What, the How, and the Why Not? LNCS, vol. 11200, pp. 390–416. Springer, Cham (2019). https://doi.org/10.1007/978-3-030-22348-9_23

    Chapter  Google Scholar 

  32. Pressman, I., Singmaster, D.: The jealous husbands and the missionaries and cannibals. Math. Gaz. 73(464), 73–81 (1989). https://doi.org/10.2307/3619658

    Article  Google Scholar 

  33. Qin, X., Bliudze, S., Madelaine, E., Hou, Z., Deng, Y., Zhang, M.: SMT-based generation of symbolic automata. Acta Inform. 57(3), 627–656 (2020). https://doi.org/10.1007/s00236-020-00367-6

    Article  Google Scholar 

  34. Rosenberg, J., et al.: SIP: Session initiation protocol. RFC 3261, RFC Editor, June 2002. https://doi.org/10.17487/RFC3261

  35. Saint-Andre, P.: Extensible messaging and presence protocol (XMPP): Core. RFC 6120, RFC Editor, March 2011. https://doi.org/10.17487/RFC6120

  36. Sakamoto, H., Ikeda, D.: Intractability of decision problems for finite-memory automata. Theor. Comput. Sci. 231(2), 297–308 (2000). https://doi.org/10.1016/S0304-3975(99)00105-X

    Article  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. TU Dortmund University, Dortmund, Germany

    Simon Dierl & Falk Howar

  2. Fraunhofer ISST, Dortmund, Germany

    Falk Howar

Authors
  1. Simon Dierl
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Falk Howar
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding authors

Correspondence to Simon Dierl or Falk Howar .

Editor information

Editors and Affiliations

  1. Faculty of Informatics, TU Wien, Vienna, Austria

    Laura Kovács

  2. Royal Institute of Technology, Stockholm, Sweden

    Karl Meinke

Rights and permissions

Reprints and permissions

Copyright information

© 2022 The Author(s), under exclusive license to Springer Nature Switzerland AG

About this paper

Check for updates. Verify currency and authenticity via CrossMark

Cite this paper

Dierl, S., Howar, F. (2022). \(\textsc {Reach}\) on Register Automata via History Independence. In: Kovács, L., Meinke, K. (eds) Tests and Proofs. TAP 2022. Lecture Notes in Computer Science, vol 13361. Springer, Cham. https://doi.org/10.1007/978-3-031-09827-7_2

Download citation

  • DOI: https://doi.org/10.1007/978-3-031-09827-7_2

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-031-09826-0

  • Online ISBN: 978-3-031-09827-7

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics