Descriptional Complexity of Iterated Uniform Finite-State Transducers

  • Martin Kutrib
  • Andreas Malcher
  • Carlo MereghettiEmail author
  • Beatrice Palano
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 11612)


We introduce the deterministic computational model of an iterated uniform finite-state transducer (iufst). A iufst performs the same length-preserving transduction on several left-to-right sweeps. The first sweep takes place on the input string, while any other sweep processes the output of the previous one. The iufst accepts or rejects upon halting in an accepting or rejecting state along its sweeps. First, we focus on constant sweep bounded iufsts. We study their descriptional power vs. deterministic finite automata, and the state cost of implementing language operations. Then, we focus on non-constant sweep bounded iufsts, showing a nonregular language hierarchy depending on sweep complexity. The hardness of some classical decision problems on constant sweep bounded iufsts is also investigated.


Iterated transducers State complexity Sweep complexity Decidability 



The authors wish to thank the anonymous referees for useful and kind comments.


  1. 1.
    Bednárová, Z., Geffert, V., Mereghetti, C., Palano, B.: The size-cost of Boolean operations on constant height deterministic pushdown automata. Theor. Comput. Sci. 449, 23–36 (2012). Scholar
  2. 2.
    Bianchi, M.P., Mereghetti, C., Palano, B.: Complexity of Promise Problems on Classical and Quantum Automata. In: Calude, C.S., Freivalds, R., Kazuo, I. (eds.) Computing with New Resources. LNCS, vol. 8808, pp. 161–175. Springer, Cham (2014). Scholar
  3. 3.
    Bordihn, H., Fernau, H., Holzer, M., Manca, V., Martín-Vide, C.: Iterated sequential transducers as language generating devices. Theor. Comput. Sci. 369(1–3), 67–81 (2006). Scholar
  4. 4.
    Citrini, C., Crespi-Reghizzi, S., Mandrioli, D.: On deterministic multi-pass analysis. SIAM J. Comput. 15(3), 668–693 (1986). Scholar
  5. 5.
    Friburger, N., Maurel, D.: Finite-state transducer cascades to extract named entities in texts. Theor. Comput. Sci. 313(1), 93–104 (2004). Scholar
  6. 6.
    Gao, Y., Moreira, N., Reis, R., Yu, S.: A survey on operational state complexity. J. Autom. Lang. Comb. 21(4), 251–310 (2017)MathSciNetzbMATHGoogle Scholar
  7. 7.
    Ginzburg, A.: Algebraic Theory of Automata. Academic Press (1968)Google Scholar
  8. 8.
    Hartmanis, J., Stearns, R.E.: Algebraic Structure Theory of Sequential Machines. Prentice-Hall (1966)Google Scholar
  9. 9.
    Hartmanis, J.: Computational complexity of one-tape turing machine computations. J. ACM 15(2), 325–339 (1968). Scholar
  10. 10.
    Holzer, M., Kutrib, M.: Descriptional complexity - an introductory survey. In: Martín-Vide, C. (ed.) Scientific Applications of Language Methods, pp. 1–58. Imperial College Press (2010)Google Scholar
  11. 11.
    Jones, N.D.: Space-bounded reducibility among combinatorial problems. J. Comput. System Sci. 11(1), 68–85 (1975)MathSciNetCrossRefGoogle Scholar
  12. 12.
    Jones, N.D., Laaser, W.T.: Complete problems for deterministic polynomial time. Theor. Comput. Sci. 3(1), 105–117 (1976)MathSciNetCrossRefGoogle Scholar
  13. 13.
    Malcher, A., Mereghetti, C., Palano, B.: Descriptional complexity of two-way pushdown automata with restricted head reversals. Theor. Comput. Sci. 449, 119–133 (2012). Scholar
  14. 14.
    Manca, V.: On the generative power of iterated transductions. In: Ito, M., Paun, G., Yu, S. (eds.) Words, Semigroups, and Transductions - Festschrift in Honor of Gabriel Thierrin, pp. 315–327. World Scientific (2001)Google Scholar
  15. 15.
    Mealy, G.H.: A method for synthesizing sequential circuits. Bell Syst. Tech. J. 34, 1045–1079 (1955). Scholar
  16. 16.
    Pierce, A.: Decision problems on iterated length-preserving transducers. Bachelor’s thesis, SCS Carnegie Mellon University, Pittsburgh (2011)Google Scholar
  17. 17.
    Salomaa, A., Wood, D., Yu, S.: On the state complexity of reversals of regular languages. Theor. Comput. Sci. 320(2–3), 315–329 (2004)MathSciNetCrossRefGoogle Scholar

Copyright information

© IFIP International Federation for Information Processing 2019

Authors and Affiliations

  1. 1.Institut für InformatikUniversität GiessenGiessenGermany
  2. 2.Dipartimento di Fisica “Aldo Pontremoli”Università degli Studi di MilanoMilanoItaly
  3. 3.Dipartimento di Informatica “G. degli Antoni”Università degli Studi di MilanoMilanoItaly

Personalised recommendations