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Theoretical Aspects of Symbolic Automata

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SOFSEM 2018: Theory and Practice of Computer Science (SOFSEM 2018)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 10706))

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Abstract

Symbolic finite automata extend classical automata by allowing infinite alphabets given by Boolean algebras and having transitions labeled by predicates over such algebras. Symbolic automata have been intensively studied recently and they have proven useful in several applications. We study some theoretical aspects of symbolic automata. Especially, we study minterms of symbolic automata, that is, the set of maximal satisfiable Boolean combinations of predicates of automata. We define canonical minterms of a language accepted by a symbolic automaton and show that these minterms can be used to define symbolic versions of some known classical automata. Also we show that canonical minterms have an important role in finding minimal nondeterministic symbolic automata. We show that Brzozowski’s double-reversal method for minimizing classical deterministic automata as well as its generalization is applicable for symbolic automata.

This work was supported by the Estonian Ministry of Education and Research institutional research grant IUT33-13.

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References

  1. Brzozowski, J.A., Tamm, H.: Theory of átomata. Theor. Comput. Sci. 539, 13–27 (2014)

    Article  MATH  Google Scholar 

  2. Brzozowski, J.A.: Canonical regular expressions and minimal state graphs for definite events. In: Proceedings of the Symposium on Mathematical Theory of Automata, MRI Symposia Series, vol. 12, pp. 529–561. Polytechnic Press, Polytechnic Institute of Brooklyn, NY (1963)

    Google Scholar 

  3. Brzozowski, J.A.: Derivatives of regular expressions. J. ACM 11(4), 481–494 (1964)

    Article  MathSciNet  MATH  Google Scholar 

  4. D’Antoni, L., Veanes, M.: The power of symbolic automata and transducers. In: Majumdar, R., Kunčak, V. (eds.) CAV 2017. LNCS, vol. 10426, pp. 47–67. Springer, Cham (2017). https://doi.org/10.1007/978-3-319-63387-9_3

    Chapter  Google Scholar 

  5. D’Antoni, L., Veanes, M.: Minimization of symbolic automata. In: The 41st Annual ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages, POPL 2014, San Diego, CA, USA, 20–21 January 2014, pp. 541–554 (2014)

    Google Scholar 

  6. D’Antoni, L., Veanes, M.: Forward bisimulations for nondeterministic symbolic finite automata. In: Tools and Algorithms for the Construction and Analysis of Systems - 23rd International Conference, TACAS 2017, ETAPS 2017, Proceedings, Part I, Uppsala, Sweden, 22–29 April 2017, pp. 518–534 (2017)

    Google Scholar 

  7. Denis, F., Lemay, A., Terlutte, A.: Residual finite state automata. Fund. Informaticae 51, 339–368 (2002)

    MathSciNet  MATH  Google Scholar 

  8. Denis, F., Lemay, A., Terlutte, A.: Learning regular languages using RFSAs. Theor. Comput. Sci. 313(2), 267–294 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  9. Drews, S., D’Antoni, L.: Learning symbolic automata. In: Legay, A., Margaria, T. (eds.) TACAS 2017. LNCS, vol. 10205, pp. 173–189. Springer, Heidelberg (2017). https://doi.org/10.1007/978-3-662-54577-5_10

    Chapter  Google Scholar 

  10. Iván, S.: Complexity of atoms, combinatorially. Inf. Process. Lett. 116, 356–360 (2016)

    Article  MathSciNet  MATH  Google Scholar 

  11. Keil, M., Thiemann, P.: Symbolic solving of extended regular expression inequalities. In: 34th International Conference on Foundation of Software Technology and Theoretical Computer Science, FSTTCS 2014, 15–17 December 2014, New Delhi, India, pp. 175–186 (2014)

    Google Scholar 

  12. Owens, S., Reppy, J., Turon, A.: Regular-expression derivatives re-examined. J. Funct. Programm. 19(2), 173–190 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  13. Tamm, H.: Generalization of the double-reversal method of finding a canonical residual finite state automaton. In: Shallit, J., Okhotin, A. (eds.) DCFS 2015. LNCS, vol. 9118, pp. 268–279. Springer, Cham (2015). https://doi.org/10.1007/978-3-319-19225-3_23

    Chapter  Google Scholar 

  14. Tamm, H.: New interpretation and generalization of the Kameda-Weiner method. In: 43rd International Colloquium on Automata, Languages, and Programming (ICALP 2016). Leibniz International Proceedings in Informatics (LIPIcs), vol. 55, Dagstuhl, Germany, Schloss Dagstuhl-Leibniz-Zentrum für Informatik, pp. 116:1–116:12 (2016)

    Google Scholar 

  15. Thompson, K.: Regular expression search algorithm. Commun. ACM 11(6), 419–422 (1968)

    Article  MATH  Google Scholar 

  16. Veanes, M., de Halleux, P., Tillmann, N.: Rex: symbolic regular expression explorer. In: Third International Conference on Software Testing, Verification and Validation, ICST 2010, pp. 498–507. IEEE Computer Society (2010)

    Google Scholar 

  17. Watson, B.W.: A taxonomy of finite automata construction algorithms. Computing science report 93/43. Eindhoven University of Technology (1995)

    Google Scholar 

  18. Watson, B.W.: Implementing and using finite automata toolkits. In: Extended finite state models of language, pp. 19–36. Cambridge University Press (1999)

    Google Scholar 

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Authors and Affiliations

  1. Tallinn University of Technology, Tallinn, Estonia

    Hellis Tamm

  2. Microsoft Research, Redmond, USA

    Margus Veanes

Authors
  1. Hellis Tamm
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  2. Margus Veanes
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Corresponding author

Correspondence to Hellis Tamm .

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Editors and Affiliations

  1. Vienna University of Technology , Vienna, Austria

    A Min Tjoa

  2. ISAE-ENSMA, Chasseneuil-du-Poitou, France

    Ladjel Bellatreche

  3. Vienna University of Technology, Vienna, Austria

    Stefan Biffl

  4. Utrecht University, Utrecht, The Netherlands

    Jan van Leeuwen

  5. Academy of Sciences, Prague, Czech Republic

    Jiří Wiedermann

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Tamm, H., Veanes, M. (2018). Theoretical Aspects of Symbolic Automata. In: Tjoa, A., Bellatreche, L., Biffl, S., van Leeuwen, J., Wiedermann, J. (eds) SOFSEM 2018: Theory and Practice of Computer Science. SOFSEM 2018. Lecture Notes in Computer Science(), vol 10706. Edizioni della Normale, Cham. https://doi.org/10.1007/978-3-319-73117-9_30

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  • DOI: https://doi.org/10.1007/978-3-319-73117-9_30

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  • Publisher Name: Edizioni della Normale, Cham

  • Print ISBN: 978-3-319-73116-2

  • Online ISBN: 978-3-319-73117-9

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