Skip to main content

Symbolic Tree Transducers

  • Conference paper
Perspectives of Systems Informatics (PSI 2011)

Part of the book series: Lecture Notes in Computer Science ((LNISA,volume 7162))

Abstract

Symbolic transducers are useful in the context of web security as they form the foundation for sanitization of potentially malicious data. We define Symbolic Tree Transducers as a generalization of Regular Transducers as finite state input-output tree automata with logical constraints over a parametric background theory. We examine key closure properties of Symbolic Tree Transducers and we develop a composition algorithm and an equivalence decision procedure for linear single-valued transducers.

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

Access this chapter

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.

References

  1. Alur, R., Cerný, P.: Streaming transducers for algorithmic verification of single-pass list-processing programs. In: 38th ACM SIGACT-SIGPLAN Symposium on Princples of Programming Languages (POPL 2011), pp. 599–610. ACM (2011)

    Google Scholar 

  2. Arnold, A., Dauchet, M.: Bi-transductions de forêts. In: Proc. 3rd International Colloquium on Automata, Languages and Programming (ICALP 1976), pp. 74–86. Edinburgh University Press, Edinburgh (1976)

    Google Scholar 

  3. Baker, B.S.: Composition of top-down and bottom-up tree transductions. Inform. and Control 41, 186–213 (1979)

    Article  MathSciNet  MATH  Google Scholar 

  4. Choffrut, C.: Minimizing subsequential transducers: a survey. Theoretical Computer Science 292(1), 131–143 (2003)

    Article  MathSciNet  MATH  Google Scholar 

  5. Courcelle, B., Franchi-Zannettacchi, P.: Attribute grammars and recursive program schemes. Theoretical Computer Science 17, 163–191 (1982)

    Article  MathSciNet  Google Scholar 

  6. de Moura, L., Bjørner, N.: Z3: An Efficient SMT Solver. In: Ramakrishnan, C.R., Rehof, J. (eds.) TACAS 2008. LNCS, vol. 4963, pp. 337–340. Springer, Heidelberg (2008)

    Chapter  Google Scholar 

  7. Engelfriet, J.: Bottom-up and top-down tree transformations – a comparison. Math. Systems Theory 9, 198–231 (1975)

    Article  MathSciNet  MATH  Google Scholar 

  8. Engelfriet, J.: Some open questions and recent results on tree transducers and tree languages. In: Book, R.V. (ed.) Formal Language Theory, pp. 241–286. Academic Press, New York (1980)

    Google Scholar 

  9. Engelfriet, J., Maneth, S.: Macro tree transducers, attribute grammars, and mso definable tree translations. Information and Computation 154, 34–91 (1999)

    Article  MathSciNet  MATH  Google Scholar 

  10. Engelfriet, J., Maneth, S.: A comparison of pebble tree transducers with macro tree transducers. Acta Informatica 39 (2003)

    Google Scholar 

  11. Engelfriet, J., Maneth, S., Seidl, H.: Deciding equivalence of top-down XML transformations in polynomial time. Journal of Computer and System Science 75(5), 271–286 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  12. Engelfriet, J., Vogler, H.: Macro tree transducers. J. Comp. and Syst. Sci. 31, 71–146 (1985)

    Article  MathSciNet  MATH  Google Scholar 

  13. Esik, Z.: Decidability results concerning tree transducers. Acta Cybernetica 5, 1–20 (1980)

    MathSciNet  MATH  Google Scholar 

  14. Fülöp, Z.: On attributed tree transducers. Acta Cybernetica 5, 261–279 (1981)

    MATH  Google Scholar 

  15. Fülöp, Z., Vogler, H.: Syntax-Directed Semantics: Formal Models Based on Tree Transducers. EATCS. Springer, Heidelberg (1998)

    MATH  Google Scholar 

  16. Gécseg, F., Steinby, M.: Tree Automata. Akadémiai Kiadó, Budapest (1984)

    MATH  Google Scholar 

  17. Griffiths, T.: The unsolvability of the equivalence problem for Λ-free nondeterministic generalized machines. J. ACM 15, 409–413 (1968)

    Article  MATH  Google Scholar 

  18. Hodges, W.: Model theory. Cambridge Univ. Press (1995)

    Google Scholar 

  19. Hooimeijer, P., Livshits, B., Molnar, D., Saxena, P., Veanes, M.: Fast and precise sanitizer analysis with Bek. In: 20th USENIX Security Symposium, pp. 1–16. USENIX Association, San Francisco (2011)

    Google Scholar 

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

    Google Scholar 

  21. 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)

    Article  MathSciNet  Google Scholar 

  22. Inaba, K., Hosoya, H.: Multi-return macro tree transducers. In: Proc. 6th ACM SIGPLAN Workshop on Programming Language Technologies for XML, San Francisco, California (January 2008)

    Google Scholar 

  23. Kobayashi, N., Tabuchi, N., Unno, H.: Higher-order multi-parameter tree transducers and recursion schemes for program verification. In: Proceedings of the 37th Annual ACM SIGPLAN-SIGACT Symposium on Principles of Programming Languages, POPL 2010, pp. 495–508. ACM (2010)

    Google Scholar 

  24. Laurence, G., Lemay, A., Niehren, J., Staworko, S., Tommasi, M.: Normalization of Sequential Top-Down Tree-to-Word Transducers. In: Dediu, A.-H., Inenaga, S., Martín-Vide, C. (eds.) LATA 2011. LNCS, vol. 6638, pp. 354–365. Springer, Heidelberg (2011)

    Chapter  Google Scholar 

  25. Maletti, A., Graehl, J., Hopkins, M., Knight, K.: The power of extended top-down tree transducers. SIAM J. Comput. 39, 410–430 (2009)

    Article  MathSciNet  MATH  Google Scholar 

  26. Milo, T., Suciu, D., Vianu, V.: Typechecking for XML transformers. In: Proc. 19th ACM Symposium on Principles of Database Systems (PODS 2000), pp. 11–22. ACM (2000)

    Google Scholar 

  27. Noord, G.V., Gerdemann, D.: Finite state transducers with predicates and identities. Grammars 4, 263–286 (2001)

    Article  MathSciNet  MATH  Google Scholar 

  28. Ong, C.-H.L., Ramsay, S.J.: Verifying higher-order functional programs with pattern-matching algebraic data types. In: 38th ACM SIGACT-SIGPLAN Symposium on Princples of Programming Languages (POPL 2011), pp. 587–598. ACM (2011)

    Google Scholar 

  29. Perst, T., Seidl, H.: Macro forest transducers. Information Processing Letters 89(3), 141–149 (2004)

    Article  MathSciNet  MATH  Google Scholar 

  30. Rounds, W.C.: Context-free grammars on trees. In: Proc. ACM Symp. on Theory of Comput., pp. 143–148. ACM (1969)

    Google Scholar 

  31. Seidl, H.: Equivalence of finite-valued tree transducers is decidable. Math. Systems Theory 27, 285–346 (1994)

    Article  MathSciNet  MATH  Google Scholar 

  32. Thatcher, J.W.: Generalized sequential machine maps. J. Comput. Syst. Sci. 4, 339–367 (1970)

    Article  MathSciNet  MATH  Google Scholar 

  33. Veanes, M., Bjørner, N.: Symbolic tree automata. Submitted to Information Processing Letters (2011)

    Google Scholar 

  34. Veanes, M., Bjørner, N., de Moura, L.: Symbolic Automata Constraint Solving. In: Fermüller, C.G., Voronkov, A. (eds.) LPAR-17. LNCS, vol. 6397, pp. 640–654. Springer, Heidelberg (2010)

    Chapter  Google Scholar 

  35. 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 

  36. Yu, S.: Regular languages. In: Rozenberg, G., Salomaa, A. (eds.) Handbook of Formal Languages, vol. 1, pp. 41–110. Springer, Heidelberg (1997)

    Chapter  Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Editor information

Editors and Affiliations

Rights and permissions

Reprints and permissions

Copyright information

© 2012 Springer-Verlag Berlin Heidelberg

About this paper

Cite this paper

Veanes, M., Bjørner, N. (2012). Symbolic Tree Transducers. In: Clarke, E., Virbitskaite, I., Voronkov, A. (eds) Perspectives of Systems Informatics. PSI 2011. Lecture Notes in Computer Science, vol 7162. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-29709-0_32

Download citation

  • DOI: https://doi.org/10.1007/978-3-642-29709-0_32

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-29708-3

  • Online ISBN: 978-3-642-29709-0

  • eBook Packages: Computer ScienceComputer Science (R0)

Publish with us

Policies and ethics