Skip to main content
SpringerLink
Log in

Decision Problems for Finite Automata over Infinite Algebraic Structures

  • Conference paper
  • First Online:
Implementation and Application of Automata (CIAA 2016)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9705))

Included in the following conference series:

Abstract

We introduce the concept of finite automata over algebraic structures. We address the classical emptiness problem and its various refinements in our setting. In particular, we prove several decidability and undecidability results. We also explain the way our automata model connects with the existential first order theory of algebraic structures.

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
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

Similar content being viewed by others

References

  1. Alur, R., Černý, P., Weinstein, S.: Algorithmic analysis of array-accessing programs. In: Grädel, E., Kahle, R. (eds.) CSL 2009. LNCS, vol. 5771, pp. 86–101. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  2. Blum, L., Shub, M., Smale, S.: On a theory of computation and complexity over the real numbers: NP-completeness, recursive functions and universal machines. Bull. Am. Math. Soc. 21(1), 1–46 (1989)

    Article  MathSciNet  MATH  Google Scholar 

  3. Bojanczyk, M., Muscholl, A., Schwentick, T., Segoufin, L., David, C.: Two-variable logic on words with data. In: Proceedings of LICS 2006, pp. 7–16 (2006)

    Google Scholar 

  4. Bojanczyk, M., David, C., Muscholl, M., Schwentick, T., Segoufin, L.: Two-variablelogic on data trees and XML reasoning. In: Proceedings of PODS 2006, pp. 10–19 (2006)

    Google Scholar 

  5. Bournez, O., Cucker, F., de Naurois, P.J., Marion, J.-Y.: Computability over an arbitrary structure. Sequential and parallel polynomial time. In: Gordon, A.D. (ed.) FOSSACS 2003. LNCS, vol. 2620, pp. 185–199. Springer, Heidelberg (2003)

    Google Scholar 

  6. Bozga, M., Iosif, R., Lakhnech, Y.: Flat parametric counter automata. In: Bugliesi, M., Preneel, B., Sassone, V., Wegener, I. (eds.) ICALP 2006. LNCS, vol. 4052, pp. 577–588. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  7. Calude, C., Calude, E., Khoussainov, B.: Deterministic automata: simulation and minimality. Ann. Pure Appl. Logic 90(1–3), 263–276 (1997)

    Article  MathSciNet  MATH  Google Scholar 

  8. Calude, C., Calude, E., Khoussainov, B.: Finite nondeterministic automata: simulation and minimality. Theor. Comput. Sci. 242(1–2), 219–235 (2000)

    Article  MathSciNet  MATH  Google Scholar 

  9. Comon, S., Jurski, Y.: Multiple counters automata, safety analysis and Presburger arithmetic. In: Hu, A.J., Vardi, M.Y. (eds.) CAV 1998. LNCS, vol. 1427, pp. 268–279. Springer, Heidelberg (1998)

    Chapter  Google Scholar 

  10. Figueira, D.: Reasoning on words and trees with data. Ph.D. thesis, ENS Cachan, France (2010)

    Google Scholar 

  11. Gandhi, A., Khoussainov, B., Liu, J.: Finite automata over structures (Extended Abstract). In: Agrawal, M., Cooper, S.B., Li, A. (eds.) TAMC 2012. LNCS, vol. 7287, pp. 373–384. Springer, Heidelberg (2012)

    Chapter  Google Scholar 

  12. Ibarra, O.: Reversal-bounded multicounter machines and their decision problems. J. ACM 25(1), 116–133 (1978)

    Article  MathSciNet  MATH  Google Scholar 

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

    Article  MathSciNet  MATH  Google Scholar 

  14. Khoussainov, B., Nerode, A.: Open questions in the theory of automatic structures. Bull. Eur. Assoc. Theor. Comput. Sci. (EATCS) (94):181–204 (2008)

    Google Scholar 

  15. Leroux, J., Sutre, G.: Flat counter automata almost everywhere!. In: Peled, D.A., Tsay, Y.-K. (eds.) ATVA 2005. LNCS, vol. 3707, pp. 489–503. Springer, Heidelberg (2005)

    Chapter  Google Scholar 

  16. Matiyasevich, Y.: Hilbert’s Tenth Problem. MIT Press, Massachusetts (1993)

    MATH  Google Scholar 

  17. Minsky, M.: Recursive unsolvability of post’s problem of “Tag” and other topics in theory of turing machines. Ann. Math. 74(3), 437–455 (1961)

    Article  MathSciNet  MATH  Google Scholar 

  18. Meer, K., Naif, A.: Generalised finite automata over real and complex numbers. Theor. Comput. Sci. 591(C), 86–98 (2015)

    MathSciNet  MATH  Google Scholar 

  19. Meer, K., Naif, A.: Periodic generalized automata over the reals. In: Dediu, A.-H., et al. (eds.) LATA 2016. LNCS, vol. 9618, pp. 168–180. Springer, Heidelberg (2016). doi:10.1007/978-3-319-30000-9_13

    Chapter  Google Scholar 

  20. Neven, F., Schwentick, T., Vianu, V.: Finite state machines for strings over infinite alphabets. ACM Trans. Comput. Logic 15(3), 403–435 (2004)

    Article  MathSciNet  Google Scholar 

  21. Segoufin, L.: Automata and logics for words and trees over an infinite alphabet. In: Ésik, Z. (ed.) CSL 2006. LNCS, vol. 4207, pp. 41–57. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  22. Segoufin, L., Torunczyk, S.: Automata based verification over linearly ordered data domains. In: Proceedings of STACS, pp. 81–92. Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik (2011)

    Google Scholar 

  23. Tan, T.: Graph reachability and pebble automata over infinite alphabets. In: Proceedings of LICS, pp. 157–166. IEEE Computer Society (2009)

    Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Computer Science, University of Auckland, Auckland, New Zealand

    Bakhadyr Khoussainov & Jiamou Liu

Authors
  1. Bakhadyr Khoussainov
    View author publications

    You can also search for this author in PubMed Google Scholar

  2. Jiamou Liu
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Bakhadyr Khoussainov .

Editor information

Editors and Affiliations

  1. Yonsei University, Seoul, Korea (Republic of)

    Yo-Sub Han

  2. Queen's University , Kingston, Ontario, Canada

    Kai Salomaa

Rights and permissions

Reprints and permissions

Copyright information

© 2016 Springer International Publishing Switzerland

About this paper

Cite this paper

Khoussainov, B., Liu, J. (2016). Decision Problems for Finite Automata over Infinite Algebraic Structures. In: Han, YS., Salomaa, K. (eds) Implementation and Application of Automata. CIAA 2016. Lecture Notes in Computer Science(), vol 9705. Springer, Cham. https://doi.org/10.1007/978-3-319-40946-7_1

Download citation

  • DOI: https://doi.org/10.1007/978-3-319-40946-7_1

  • Published:

  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-40945-0

  • Online ISBN: 978-3-319-40946-7

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics

Search

Navigation