Skip to main content

Exact DFA Identification Using SAT Solvers

  • Conference paper
Grammatical Inference: Theoretical Results and Applications (ICGI 2010)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 6339))

Included in the following conference series:

Abstract

We present an exact algorithm for identification of deterministic finite automata (DFA) which is based on satisfiability (SAT) solvers. Despite the size of the low level SAT representation, our approach is competitive with alternative techniques. Our contributions are fourfold: First, we propose a compact translation of DFA identification into SAT. Second, we reduce the SAT search space by adding lower bound information using a fast max-clique approximation algorithm. Third, we include many redundant clauses to provide the SAT solver with some additional knowledge about the problem. Fourth, we show how to use the flexibility of our translation in order to apply it to very hard problems. Experiments on a well-known suite of random DFA identification problems show that SAT solvers can efficiently tackle all instances. Moreover, our algorithm outperforms state-of-the-art techniques on several hard problems.

This is an extended version of: Marijn Heule and Sicco Verwer. Using a Satisfiability Solver to Identify Deterministic Finite State Automata. In BNAIC 2009, pp. 91-98.

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

Access this chapter

Subscribe and save

Springer+ Basic
EUR 32.99 /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 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

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

Similar content being viewed by others

References

  1. de la Higuera, C.: A bibliographical study of grammatical inference. Pattern Recognition 38(9), 1332–1348 (2005)

    Article  Google Scholar 

  2. Gold, E.M.: Complexity of automaton identification from given data. Information and Control 37(3), 302–320 (1978)

    Article  MATH  MathSciNet  Google Scholar 

  3. Lang, K.J., Pearlmutter, B.A., Price, R.A.: Results of the abbadingo one DFA learning competition and a new evidence-driven state merging algorithm. In: Honavar, V.G., Slutzki, G. (eds.) ICGI 1998. LNCS (LNAI), vol. 1433, p. 1. Springer, Heidelberg (1998)

    Chapter  Google Scholar 

  4. Oncina, J., Garcia, P.: Inferring regular languages in polynomial update time. In: Pattern Recognition and Image Analysis. Series in Machine Perception and Artificial Intelligence, vol. 1, pp. 49–61. World Scientific, Singapore (1992)

    Chapter  Google Scholar 

  5. Oliveira, A.L., Marques-Silva, J.P.: Efficient search techniques for the inference of minimum sized finite state machines. In: SPIRE, pp. 81–89 (1998)

    Google Scholar 

  6. Abela, J., Coste, F., Spina, S.: Mutually compatible and incompatible merges for the search of the smallest consistent DFA. In: Paliouras, G., Sakakibara, Y. (eds.) ICGI 2004. LNCS (LNAI), vol. 3264, pp. 28–39. Springer, Heidelberg (2004)

    Google Scholar 

  7. Lang, K.J.: Faster algorithms for finding minimal consistent DFAs. Technical report, NEC Research Institute (1999)

    Google Scholar 

  8. Bugalho, M., Oliveira, A.L.: Inference of regular languages using state merging algorithms with search. Pattern Recognition 38, 1457–1467 (2005)

    Article  MATH  Google Scholar 

  9. Biere, A., Cimatti, A., Clarke, E.M., Zhu, Y.: Symbolic model checking without BDDs. In: Cleaveland, W.R. (ed.) TACAS 1999. LNCS, vol. 1579, pp. 193–207. Springer, Heidelberg (1999)

    Chapter  Google Scholar 

  10. Marques-Silva, J.P., Glass, T.: Combinational equivalence checking using satisfiability and recursive learning. In: DATE 1999, p. 33. ACM, New York (1999)

    Chapter  Google Scholar 

  11. Endrullis, J., Waldmann, J., Zantema, H.: Matrix interpretations for proving termination of term rewriting. J. Autom. Reason. 40(2-3), 195–220 (2008)

    Article  MATH  MathSciNet  Google Scholar 

  12. Coste, F., Nicolas, J.: Regular inference as a graph coloring problem. In: Workshop on Grammatical Inference, Automata Induction, and Language Acquisition, ICML 1997 (1997)

    Google Scholar 

  13. Grinchtein, O., Leucker, M., Piterman, N.: Inferring network invariants automatically. In: Furbach, U., Shankar, N. (eds.) IJCAR 2006. LNCS (LNAI), vol. 4130, pp. 483–497. Springer, Heidelberg (2006)

    Chapter  Google Scholar 

  14. Biermann, A.W., Feldman, J.A.: On the synthesis of finite-state machines from samples of their behavior. IEEE Trans. Comput. 21(6), 592–597 (1972)

    Article  MATH  MathSciNet  Google Scholar 

  15. Walsh, T.: SAT v CSP. In: Dechter, R. (ed.) CP 2000. LNCS, vol. 1894, pp. 441–456. Springer, Heidelberg (2000)

    Chapter  Google Scholar 

  16. Sakallah, K.A.: Symmetry and Satisfiability. In: Handbook of Satisfiability, ch. 10, pp. 289–338. IOS Press, Amsterdam (2009)

    Google Scholar 

  17. Kullmann, O.: On a generalization of extended resolution. Discrete Applied Mathematics 96-97(1), 149–176 (1999)

    Article  MathSciNet  Google Scholar 

  18. Jarvisalo, M., Biere, A., Heule, M.J.H.: Blocked clause elimination. In: Esparza, J., Majumdar, R. (eds.) TACAS 2010. LNCS, vol. 6015, pp. 129–144. Springer, Heidelberg (2010)

    Google Scholar 

  19. Oliveira, A.L., Marques-Silva, J.P.: Efficient search techniques for the inference of minimum size finite automata. In: South American Symposium on String Processing and Information Retrieval, pp. 81–89. IEEE Computer Society Press, Los Alamitos (1998)

    Chapter  Google Scholar 

  20. Biere, A.: Picosat essentials. Journal on Satisfiability, Boolean Modeling and Computation 4, 75–97 (2008)

    MATH  Google Scholar 

  21. Velev, M.N.: Exploiting hierarchy and structure to efficiently solve graph coloring as sat. In: ICCAD 2007: International conference on Computer-aided design, Piscataway, NJ, USA, pp. 135–142. IEEE Press, Los Alamitos (2007)

    Chapter  Google Scholar 

  22. Schaafsma, B., Heule, M.J.H., van Maaren, H.: Dynamic symmetry breaking by simulating Zykov contraction. In: Kullmann, O. (ed.) SAT 2009. LNCS, vol. 5584, pp. 223–236. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2010 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Heule, M.J.H., Verwer, S. (2010). Exact DFA Identification Using SAT Solvers. In: Sempere, J.M., García, P. (eds) Grammatical Inference: Theoretical Results and Applications. ICGI 2010. Lecture Notes in Computer Science(), vol 6339. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-15488-1_7

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-15488-1_7

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-15487-4

  • Online ISBN: 978-3-642-15488-1

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics