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Brzozowski’s Minimization Algorithm—More Robust than Expected

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Implementation and Application of Automata (CIAA 2013)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 7982))

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Abstract

For a finite automaton, regardless whether it is deterministic or nondeterministic, Brzozowski’s minimization algorithm computes the equivalent minimal deterministic finite automaton by applying reversal and power-set construction twice. Although this is an exponential algorithm because of the power-set construction, it performs well in experimental studies compared to efficient O(nlogn) minimization algorithms. Here we show how to slightly enhance Brzozowski’s minimization algorithm by some sort of reachability information so that it can be applied to the following automata models: deterministic cover automata, almost equivalent deterministic finite state machines, and k-similar automata.

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References

  1. Almeida, M., Moreira, N., Reis, R.: On the performance of automata minimization algorithms. In: Beckmann, A., Dimitracopoulos, C., Löwe, B. (eds.) Proceedings of the 4th Conference on Computation in Europe: Logic and Theory of Algorithms, pp. 3–14. Technical Report, University of Athens, Athens, Greece (2008)

    Google Scholar 

  2. Badr, A., Geffert, V., Shipman, I.: Hyper-minimizing minimized deterministic finite state automata. RAIRO–Informatique Théorique et Applications / Theoretical Informatics and Applications 43(1), 69–94 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  3. Bonchi, F., Bonsangue, M.M., Rutten, J.J.M.M., Silva, A.: Brzozowski’s algorithm (co)algebraically. In: Constable, R.L., Silva, A. (eds.) Kozen Festschrift. LNCS, vol. 7230, pp. 12–23. Springer, Heidelberg (2012)

    Chapter  Google Scholar 

  4. Brzozowski, J.A.: Canonical regular expressions and minimal state graphs for definite events. Mathematical Theory of Automata, MRI Symposia Series 12, 529–561 (1962)

    Google Scholar 

  5. Câmpeanu, C., Sântean, N., Yu, S.: Minimal cover-automata for finite languages. Theoret. Comput. Sci. 267(1-2), 3–16 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  6. Castiglione, G., Restivo, A., Sciortino, M.: Nondeterministic Moore automata and Brzozowski’s minimization algorithm. Theoret. Comput. Sci. 450, 81–91 (2012)

    Article  MathSciNet  MATH  Google Scholar 

  7. Champarnaud, J.M., Khorsi, A., Paranthoën, T.: Split and join for minimization: Brzozowski’s algorithm. In: Balík, M., Šimánek, M. (eds.) Proceedings of the Prague Stringology Conference, pp. 96–104. No. DC-2002-03 in Research Report, Czech Technical University, Prague, Czech Republic (2002)

    Google Scholar 

  8. Gawrychowski, P., Jeż, A.: Hyper-minimisation made efficient. In: Královič, R., Niwiński, D. (eds.) MFCS 2009. LNCS, vol. 5734, pp. 356–368. Springer, Heidelberg (2009)

    Chapter  Google Scholar 

  9. Gawrychowski, P., Jeż, A., Maletti, A.: On minimising automata with errors. In: Murlak, F., Sankowski, P. (eds.) MFCS 2011. LNCS, vol. 6907, pp. 327–338. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

  10. Holzer, M., Jakobi, S.: From equivalence to almost-equivalence, and beyond—minimizing automata with errors. In: Yen, H.-C., Ibarra, O.H. (eds.) DLT 2012. LNCS, vol. 7410, pp. 190–201. Springer, Heidelberg (2012)

    Chapter  Google Scholar 

  11. Holzer, M., Maletti, A.: An nlogn algorithm for hyper-minimizing a (minimized) deterministic automaton. Theoret. Comput. Sci. 411(38-39), 3404–3413 (2010)

    Article  MathSciNet  MATH  Google Scholar 

  12. Hopcroft, J.E., Ullman, J.D.: Introduction to Automata Theory, Languages and Computation. Addison-Wesley (1979)

    Google Scholar 

  13. Jiang, T., Ravikumar, B.: Minimal NFA problems are hard. SIAM J. Comput. 22(6), 1117–1141 (1993)

    Article  MathSciNet  MATH  Google Scholar 

  14. Körner, H.: A time and space efficient algorithm for minimizing cover automata for finite languages. Internat. J. Found. Comput. Sci. 14(6), 1071–1086 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  15. Watson, B.W.: Taxonomies and Toolkits of Regular Language Algorithms. PhD thesis, Eindhoven University of Technology, Department of Mathematics and Computer Science, Den Dolech 2, 5612 AZ Eindhoven, The Netherlands (1995)

    Google Scholar 

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Authors and Affiliations

  1. Institut für Informatik, Universität Giessen, Arndtstr. 2, 35392, Giessen, Germany

    Markus Holzer & Sebastian Jakobi

Authors
  1. Markus Holzer
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  2. Sebastian Jakobi
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Editors and Affiliations

  1. Department of Mathematics and Computing Science, Saint Mary’s University, 923 Robie Street, NS B3H 3C3, Halifax, Canada

    Stavros Konstantinidis

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Holzer, M., Jakobi, S. (2013). Brzozowski’s Minimization Algorithm—More Robust than Expected. In: Konstantinidis, S. (eds) Implementation and Application of Automata. CIAA 2013. Lecture Notes in Computer Science, vol 7982. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-39274-0_17

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  • DOI: https://doi.org/10.1007/978-3-642-39274-0_17

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-39273-3

  • Online ISBN: 978-3-642-39274-0

  • eBook Packages: Computer ScienceComputer Science (R0)

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