Equivalence of Extended Symbolic Finite Transducers

  • Loris D’Antoni
  • Margus Veanes
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8044)

Abstract

Symbolic Finite Transducers augment classic transducers with symbolic alphabets represented as parametric theories. Such extension enables succinctness and the use of potentially infinite alphabets while preserving closure and decidability properties. Extended Symbolic Finite Transducers further extend these objects by allowing transitions to read consecutive input elements in a single step. While when the alphabet is finite this extension does not add expressiveness, it does so when the alphabet is symbolic. We show how such increase in expressiveness causes decision problems such as equivalence to become undecidable and closure properties such as composition to stop holding. We also investigate how the automata counterpart, Extended Symbolic Finite Automata, differs from Symbolic Finite Automata. We then introduce the subclass of Cartesian Extended Symbolic Finite Transducers in which guards are limited to conjunctions of unary predicates. Our main result is an equivalence algorithm for such subclass in the single-valued case. Finally, we model real world problems with Cartesian Extended Symbolic Finite Transducers and use the equivalence algorithm to prove their correctness.

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References

  1. 1.
    Alur, R., Cerný, P.: Streaming transducers for algorithmic verification of single-pass list-processing programs. In: POPL 2011, pp. 599–610. ACM (2011)Google Scholar
  2. 2.
    Botincan, M., Babic, D.: Sigma*: symbolic learning of input-output specifications. In: POPL 2013, pp. 443–456. ACM (2013)Google Scholar
  3. 3.
    Culic, K., Karhumäki, J.: The equivalence of finite-valued transducers (on HDTOL languages) is decidable. Theoretical Computer Science 47, 71–84 (1986)MathSciNetCrossRefGoogle Scholar
  4. 4.
    D’Antoni, L., Veanes, M.: Static analysis of string encoders and decoders. In: Giacobazzi, R., Berdine, J., Mastroeni, I. (eds.) VMCAI 2013. LNCS, vol. 7737, pp. 209–228. Springer, Heidelberg (2013)CrossRefGoogle Scholar
  5. 5.
    Fülöp, Z., Vogler, H.: Syntax-Directed Semantics: Formal Models Based on Tree Transducers. EATCS (1998)Google Scholar
  6. 6.
    Griffiths, T.: The unsolvability of the equivalence problem for Λ-free nondeterministic generalized machines. J. ACM 15, 409–413 (1968)CrossRefMATHGoogle Scholar
  7. 7.
    Hooimeijer, P., Livshits, B., Molnar, D., Saxena, P., Veanes, M.: Fast and precise sanitizer analysis with Bek. In: USENIX Security, pp. 1–16 (2011)Google Scholar
  8. 8.
    Ibarra, O.: The unsolvability of the equivalence problem for Efree NGSM’s with unary input (output) alphabet and applications. SIAM Journal on Computing 4, 524–532 (1978)MathSciNetCrossRefGoogle Scholar
  9. 9.
    Kaminski, M., Francez, N.: Finite-memory automata. TCS 134(2), 329–363 (1994)MathSciNetCrossRefMATHGoogle Scholar
  10. 10.
    Kumar, S., Chandrasekaran, B., Turner, J., Varghese, G.: Curing regular expressions matching algorithms from insomnia, amnesia, and acalculia. In: ANCS 2007, pp. 155–164. ACM/IEEE (2007)Google Scholar
  11. 11.
    Maletti, A., Graehl, J., Hopkins, M., Knight, K.: The power of extended top-down tree transducers. SIAM J. Comput. 39(2), 410–430 (2009)MathSciNetCrossRefMATHGoogle Scholar
  12. 12.
    Mohri, M.: Finite-state transducers in language and speech processing. Comput. Linguist. 23(2), 269–311 (1997)MathSciNetGoogle Scholar
  13. 13.
    Schützenberger, M.P.: Sur les relations rationnelles. In: Brakhage, H. (ed.) GI-Fachtagung 1975. LNCS, vol. 33, pp. 209–213. Springer, Heidelberg (1975)Google Scholar
  14. 14.
    Segoufin, L.: Automata and logics for words and trees over an infinite alphabet. In: CSL, pp. 41–57 (2006)Google Scholar
  15. 15.
    Smith, R., Estan, C., Jha, S., Kong, S.: Deflating the big bang: fast and scalable deep packet inspection with extended finite automata. In: SIGCOMM 2008, pp. 207–218. ACM (2008)Google Scholar
  16. 16.
    Veanes, M., Hooimeijer, P., Livshits, B., Molnar, D., Bjorner, N.: Symbolic finite state transducers: Algorithms and applications. In: POPL 2012, pp. 137–150. ACM (2012)Google Scholar
  17. 17.
    Weber, A.: Decomposing finite-valued transducers and deciding their equivalence. SIAM Journal on Computing 22(1), 175–202 (1993)MathSciNetCrossRefMATHGoogle Scholar
  18. 18.
    Yu, S.: Regular languages. In: Rozenberg, G., Salomaa, A. (eds.) Handbook of Formal Languages, vol. 1, pp. 41–110. Springer (1997)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2013

Authors and Affiliations

  • Loris D’Antoni
    • 1
  • Margus Veanes
    • 2
  1. 1.University of PennsylvaniaUSA
  2. 2.Microsoft ResearchUSA

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