Skip to main content
SpringerLink
Log in

An Automata-Theoretic Approach to Modeling Systems and Specifications over Infinite Data

  • Conference paper
  • First Online:
NASA Formal Methods (NFM 2017)

Part of the book series: Lecture Notes in Computer Science ((LNPSE,volume 10227))

Included in the following conference series:

Abstract

Data-parameterized systems model finite state systems over an infinite data domain. VLTL is an extension of LTL that uses variables in order to specify properties of computations over infinite data, and as such VLTL is suitable for specifying properties of data-parameterized systems. We present Alternating Variable Büchi Word Automata (AVBWs), a new model of automata over infinite alphabets, capable of modeling a significant fragment of VLTL. While alternating and non-deterministic Büchi automata over finite alphabets have the same expressive power, we show that this is not the case for infinite data domains, as we prove that AVBWs are strictly stronger than the previously defined Non-deterministic Variable Büchi Word Automata (NVBWs). However, while the emptiness problem is easy for NVBWs, it is undecidable for AVBWs. We present an algorithm for translating AVBWs to NVBWs in cases where such a translation is possible. Additionally, we characterize the structure of AVBWs that can be translated to NVBWs with our algorithm, and identify fragments of VLTL for which a direct NVBW construction exists. Since the emptiness problem is crucial in the automata-theoretic approach to model checking, our results give rise to a model-checking algorithm for a rich fragment of VLTL and systems over infinite data domains.

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

Notes

  1. 1.

    In particular, the negation operator is not included.

  2. 2.

    The semantics of \(\lnot a.x\) is regarding a specific value. I.e., if \(x=d\) then a.d does not hold, but \(a.d'\) for \(d\ne d'\) may hold.

  3. 3.

    Comments to the algorithm are given in gray.

  4. 4.

    In [17] the authors conjecture without proof that the formula \(\textsf {G}\, \exists x: a.x\) does not have an equivalent in PNF. In Lemma 1 we showed \(\textsf {G}\, \exists x(b.x\wedge \textsf {F}\, a.x)\) does not have an equivalent NVBW, thus it does not have an equivalent \(\exists ^*_{pnf}\)-VLTL formula. This is a different formula from \(\textsf {G}\, \exists x: a.x\), but the conclusion remains the same.

References

  1. Barringer, H., Falcone, Y., Havelund, K., Reger, G., Rydeheard, D.: Quantified event automata: towards expressive and efficient runtime monitors. In: Giannakopoulou, D., Méry, D. (eds.) FM 2012. LNCS, vol. 7436, pp. 68–84. Springer, Heidelberg (2012). doi:10.1007/978-3-642-32759-9_9

    Chapter  Google Scholar 

  2. Bauer, A., Leucker, M., Schallhart, C.: Runtime verification for LTL and TLTL. ACM Trans. Softw. Eng. Methodol. 20(4), 14:1–14:64 (2011)

    Article  Google Scholar 

  3. Bojańczyk, M., Muscholl, A., Schwentick, T., Segoufin, L., David, C.: Two-variable logic on words with data. In: 21st IEEE Symposium on Logic in Computer Science (LICS 2006), 12–15, Seattle, WA, USA, Proceedings, pp. 7–16. IEEE Computer Society, 2006, August 2006

    Google Scholar 

  4. Bouajjani, A., Habermehl, P., Jurski, Y., Sighireanu, M.: Rewriting systems with data. In: Csuhaj-Varjú, E., Ésik, Z. (eds.) FCT 2007. LNCS, vol. 4639, pp. 1–22. Springer, Heidelberg (2007). doi:10.1007/978-3-540-74240-1_1

    Chapter  Google Scholar 

  5. Brambilla, M., Ceri, S., Comai, S., Fraternali, P., Manolescu, I.: Specification and design of workflow-driven hypertexts. J. Web Eng. 1(2), 163–182 (2003)

    Google Scholar 

  6. J. R. Buechi. On a decision method in restricted second-order arithmetic. In International Congress on Logic, Methodology, and Philosophy of Science, pp. 1–11. Stanford University Press, (1962)

    Google Scholar 

  7. Ceri, S., Matera, M., Rizzo, F., Demaldé, V.: Designing data-intensive web applications for content accessibility using web marts. Commun. ACM 50(4), 55–61 (2007)

    Article  Google Scholar 

  8. Colin, S., Mariani, L.: Run-time verification. In: Broy, M., Jonsson, B., Katoen, J.-P., Leucker, M., Pretschner, A. (eds.) Model-Based Testing of Reactive Systems. LNCS, vol. 3472, pp. 525–555. Springer, Heidelberg (2005). doi:10.1007/11498490_24

    Chapter  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  10. Grumberg, O., Kupferman, O., Sheinvald, S.: Variable Automata over Infinite Alphabets. In: Dediu, A.-H., Fernau, H., Martín-Vide, C. (eds.) LATA 2010. LNCS, vol. 6031, pp. 561–572. Springer, Heidelberg (2010). doi:10.1007/978-3-642-13089-2_47

    Chapter  Google Scholar 

  11. Grumberg, O., Kupferman, O., Sheinvald, S.: Model checking systems and specifications with parameterized atomic propositions. In: Chakraborty, S., Mukund, M. (eds.) ATVA 2012. LNCS, pp. 122–136. Springer, Heidelberg (2012). doi:10.1007/978-3-642-33386-6_11

    Chapter  Google Scholar 

  12. Grumberg, O., Kupferman, O., Sheinvald, S.: A game-theoretic approach to simulation of data-parameterized systems. In: Cassez, F., Raskin, J.-F. (eds.) ATVA 2014. LNCS, vol. 8837, pp. 348–363. Springer, Cham (2014). doi:10.1007/978-3-319-11936-6_25

    Google Scholar 

  13. Kaminski, M., Francez, N.: Finite-memory automata. Theor. Comput. Sci. 134(2), 329–363 (1994)

    Article  MathSciNet  MATH  Google Scholar 

  14. Miyano, S., Hayashi, T.: Alternating finite automata on omega-words. Theor. Comput. Sci. 32, 321–330 (1984)

    Article  MathSciNet  MATH  Google Scholar 

  15. Muller, D., Schupp, P.E.: Alternating automata on infinite objects, determinacy and Rabin’s theorem. In: Nivat, M., Perrin, D. (eds.) LITP 1984. LNCS, vol. 192, pp. 99–107. Springer, Heidelberg (1985). doi:10.1007/3-540-15641-0_27

    Chapter  Google Scholar 

  16. Neven, F., Schwentick, T., Vianu, V.: Towards regular languages over infinite alphabets. In: Sgall, J., Pultr, A., Kolman, P. (eds.) MFCS 2001. LNCS, vol. 2136, pp. 560–572. Springer, Heidelberg (2001). doi:10.1007/3-540-44683-4_49

    Chapter  Google Scholar 

  17. Song, F., Wu, Z.: Extending temporal logics with data variable quantifications. In: Raman, V., Suresh, S.P. (eds.) 34th International Conference on Foundation of Software Technology and Theoretical Computer Science, FSTTCS 15–17, 2014, New Delhi, India, vol. 29 of LIPIcs, pp. 253–265. Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik, 2014, December 2014

    Google Scholar 

  18. Vardi, M.Y.: An automata-theoretic approach to linear temporal logic. In: Moller, F., Birtwistle, G. (eds.) Logics for Concurrency. LNCS, vol. 1043, pp. 238–266. Springer, Heidelberg (1996). doi:10.1007/3-540-60915-6_6

    Chapter  Google Scholar 

  19. Vardi, M.Y., Wolper, P.: An automata-theoretic approach to automatic program verification (preliminary report). In: Proceedings of the Symposium on Logic in Computer Science (LICS 1986), Cambridge, Massachusetts, USA, June 16–18, pp. 332–344. IEEE Computer Society (1986)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Computer Science, The Technion, Haifa, Israel

    Hadar Frenkel & Orna Grumberg

  2. Department of Software Engineering, ORT Braude Academic College, Karmiel, Israel

    Sarai Sheinvald

Authors
  1. Hadar Frenkel
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Orna Grumberg
    View author publications

    You can also search for this author in PubMed Google Scholar

  3. Sarai Sheinvald
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Hadar Frenkel .

Editor information

Editors and Affiliations

  1. Stanford University, Palo Alto, California, USA

    Clark Barrett

  2. NASA Ames Research Center, Moffett Field, California, USA

    Misty Davies

  3. NASA Ames Research Center, Moffett Field, California, USA

    Temesghen Kahsai

Rights and permissions

Reprints and permissions

Copyright information

© 2017 Springer International Publishing AG

About this paper

Cite this paper

Frenkel, H., Grumberg, O., Sheinvald, S. (2017). An Automata-Theoretic Approach to Modeling Systems and Specifications over Infinite Data. In: Barrett, C., Davies, M., Kahsai, T. (eds) NASA Formal Methods. NFM 2017. Lecture Notes in Computer Science(), vol 10227. Springer, Cham. https://doi.org/10.1007/978-3-319-57288-8_1

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-57288-8_1

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-57287-1

  • Online ISBN: 978-3-319-57288-8

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation