Copyful Streaming String Transducers

Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10506)

Abstract

Copyless streaming string transducers (copyless SST) have been introduced by R. Alur and P. Černý in 2010 as a one-way deterministic automata model to define transductions of finite strings. Copyless SST extend deterministic finite state automata with a set of variables in which to store intermediate output strings, and those variables can be combined and updated all along the run, in a linear manner, i.e., no variable content can be copied on transitions. It is known that copyless SST capture exactly the class of MSO-definable string-to-string transductions, and are as expressive as deterministic two-way transducers. They enjoy good algorithmic properties. Most notably, they have decidable equivalence problem (in PSpace).

On the other hand, HDT0L systems have been introduced for a while, the most prominent result being the decidability of the equivalence problem. In this paper, we propose a semantics of HDT0L systems in terms of transductions, and use it to study the class of deterministic copyful SST. Our contributions are as follows:
  1. (i)

    HDT0L systems and total deterministic copyful SST have the same expressive power,

     
  2. (ii)

    the equivalence problem for deterministic copyful SST and the equivalence problem for HDT0L systems are inter-reducible, in linear time. As a consequence, equivalence of deterministic SST is decidable,

     
  3. (iii)

    the functionality of non-deterministic copyful SST is decidable,

     
  4. (iv)

    determining whether a deterministic copyful SST can be transformed into an equivalent deterministic copyless SST is decidable in polynomial time.

     

References

  1. 1.
    Alur, A., Černý, P.: Streaming transducers for algorithmic verification of single-pass list-processing programs. In: POPL, pp. 599–610 (2011)Google Scholar
  2. 2.
    Alur, R., Černý, P.: Expressiveness of streaming string transducers. In: FSTTCS, vol. 8, pp. 1–12 (2010)Google Scholar
  3. 3.
    Alur, R., D’Antoni, L.: Streaming tree transducers. CoRR, abs/1104.2599 (2011)Google Scholar
  4. 4.
    Alur, R., D’Antoni, L.: Streaming tree transducers. In: Czumaj, A., Mehlhorn, K., Pitts, A., Wattenhofer, R. (eds.) ICALP 2012. LNCS, vol. 7392, pp. 42–53. Springer, Heidelberg (2012). doi:10.1007/978-3-642-31585-5_8 CrossRefGoogle Scholar
  5. 5.
    Alur, R., D’Antoni, L., Deshmukh, J.V., Raghothaman, M., Yuan, Y.: Regular functions and cost register automata. In: 28th Annual ACM/IEEE Symposium on Logic in Computer Science, LICS 2013, pp. 13–22. IEEE Computer Society (2013)Google Scholar
  6. 6.
    Alur, R., Deshmukh, J.V.: Nondeterministic streaming string transducers. In: Aceto, L., Henzinger, M., Sgall, J. (eds.) ICALP 2011. LNCS, vol. 6756, pp. 1–20. Springer, Heidelberg (2011). doi:10.1007/978-3-642-22012-8_1 CrossRefGoogle Scholar
  7. 7.
    Alur, R., Filiot, E., Trivedi, A.: Regular transformations of infinite strings. In: LICS, pp. 65–74. IEEE (2012)Google Scholar
  8. 8.
    Benedikt, M., Duff, T., Sharad, A., Worrell, J.: Polynomial automata: zeroness and applications. In: Proceedings of the 32nd Annual ACM/IEEE Symposium on Logic in Computer Science, LICS 2017. ACM (2017, to appear)Google Scholar
  9. 9.
    Culik, K., Karhumäki, J.: The equivalence of finite valued transducers (on HDT0L languages) is decidable. Theor. Comput. Sci. 47(3), 71–84 (1986)MathSciNetCrossRefMATHGoogle Scholar
  10. 10.
    Dartois, L., Filiot, E., Reynier, P.-A., Talbot, J.-M.: Two-way visibly pushdown automata and transducers. In: Proceedings of the 31st Annual ACM/IEEE Symposium on Logic in Computer Science, LICS 2016, pp. 217–226. ACM (2016)Google Scholar
  11. 11.
    Dartois, L., Jecker, I., Reynier, P.-A.: Aperiodic string transducers. In: Brlek, S., Reutenauer, C. (eds.) DLT 2016. LNCS, vol. 9840, pp. 125–137. Springer, Heidelberg (2016). doi:10.1007/978-3-662-53132-7_11 CrossRefGoogle Scholar
  12. 12.
    Engelfriet, J., Hoogeboom, H.J.: MSO definable string transductions and two-way finite-state transducers. ACM Trans. Comput. Logic 2, 216–254 (2001)MathSciNetCrossRefMATHGoogle Scholar
  13. 13.
    Engelfriet, J., Maneth, S.: Macro tree transducers, attribute grammars, and MSO definable tree translations. Inf. Comput. 154(1), 34–91 (1999)MathSciNetCrossRefMATHGoogle Scholar
  14. 14.
    Engelfriet, J., Maneth, S.: The equivalence problem for deterministic MSO tree transducers is decidable. Inf. Process. Lett. 100(5), 206–212 (2006)MathSciNetCrossRefMATHGoogle Scholar
  15. 15.
    Filiot, E., Krishna, S.N., Trivedi, A.: First-order definable string transformations. In: 34th International Conference on Foundation of Software Technology and Theoretical Computer Science, FSTTCS 2014. LIPIcs, vol. 29, pp. 147–159. Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik (2014)Google Scholar
  16. 16.
    Filiot, E., Reynier, P.-A.: Transducers, logic and algebra for functions of finite words. SIGLOG News 3(3), 4–19 (2016)Google Scholar
  17. 17.
    Griffiths, T.V.: The unsolvability of the equivalence problem for lambda-free nondeterministic generalized machines. J. ACM 15(3), 409–413 (1968)CrossRefMATHGoogle Scholar
  18. 18.
    Honkala, J.: A short solution for the HDT0L sequence equivalence problem. Theor. Comput. Sci. 244(1–2), 267–270 (2000)MathSciNetCrossRefMATHGoogle Scholar
  19. 19.
    Lindenmayer, A.: Mathematical models for cellular interaction in development. J. Theoret. Biol. 18, 280–315 (1968)CrossRefGoogle Scholar
  20. 20.
    Mandel, A., Simon, I.: On finite semigroups of matrices. Theor. Comput. Sci. 5(2), 101–111 (1977)MathSciNetCrossRefMATHGoogle Scholar
  21. 21.
    Seidl, H., Maneth, S., Kemper, G.: Equivalence of deterministic top-down tree-to-string transducers is decidable. In: IEEE 56th Annual Symposium on Foundations of Computer Science, FOCS 2015, pp. 943–962. IEEE Computer Society (2015)Google Scholar

Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  1. 1.Computer Science DepartmentUniversité Libre de BruxellesBrusselsBelgium
  2. 2.Aix-Marseille Univ, LIF, CNRSMarseilleFrance

Personalised recommendations