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Linear-Time Limited Automata

  • Bruno Guillon
  • Luca Prigioniero
Conference paper
First Online:
Part of the Lecture Notes in Computer Science book series (LNCS, volume 10952)

Abstract

The time complexity of 1-limited automata is investigated from a descriptional complexity view point. Though the model recognizes regular languages only, it may use quadratic time in the input length. We show that, with a polynomial increase in size and preserving determinism, each 1-limited automaton can be transformed into an halting linear-time equivalent one. We also obtain polynomial transformations into related models, including weight-reducing Hennie machines, and we show exponential gaps for converse transformations in the deterministic case.

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Notes

Acknowledgement

We are very indebted to Giovanni Pighizzini for suggesting the problem and for many stimulating conversations.

References

  1. 1.
    Bojańczyk, M., Daviaud, L., Guillon, B., Penelle, V.: Which classes of origin graphs are generated by transducers. In: ICALP 2017. LIPIcs, vol. 80, pp. 114:1–114:13 (2017)Google Scholar
  2. 2.
    Geffert, V., Mereghetti, C., Pighizzini, G.: Complementing two-way finite automata. Inf. Comput. 205(8), 1173–1187 (2007)MathSciNetCrossRefGoogle Scholar
  3. 3.
    Hennie, F.C.: One-tape, off-line Turing machine computations. Inf. Comput. 8(6), 553–578 (1965)MathSciNetzbMATHGoogle Scholar
  4. 4.
    Hibbard, T.N.: A generalization of context-free determinism. Inf. Comput. 11(1/2), 196–238 (1967)MathSciNetzbMATHGoogle Scholar
  5. 5.
    Hopcroft, J.E., Ullman, J.D.: Introduction to Automata Theory, Languages and Computation. Addison-Wesley, Boston (1979)zbMATHGoogle Scholar
  6. 6.
    Kapoutsis, C.A.: Predicate characterizations in the polynomial-size hierarchy. In: Beckmann, A., Csuhaj-Varjú, E., Meer, K. (eds.) CiE 2014. LNCS, vol. 8493, pp. 234–244. Springer, Cham (2014).  https://doi.org/10.1007/978-3-319-08019-2_24CrossRefGoogle Scholar
  7. 7.
    Kutrib, M., Pighizzini, G., Wendlandt, M.: Descriptional complexity of limited automata. Inf. Comput. 259(2), 259–276 (2018)MathSciNetCrossRefGoogle Scholar
  8. 8.
    Pighizzini, G.: Nondeterministic one-tape off-line Turing machines. J. Autom. Lang. Comb. 14(1), 107–124 (2009)MathSciNetzbMATHGoogle Scholar
  9. 9.
    Pighizzini, G., Pisoni, A.: Limited automata and regular languages. Int. J. Found. Comput. Sci. 25(07), 897–916 (2014)MathSciNetCrossRefGoogle Scholar
  10. 10.
    Pighizzini, G., Pisoni, A.: Limited automata and context-free languages. Fundamenta Informaticae 136(1–2), 157–176 (2015)MathSciNetzbMATHGoogle Scholar
  11. 11.
    Pighizzini, G., Prigioniero, L.: Limited automata and unary languages. In: Charlier, É., Leroy, J., Rigo, M. (eds.) DLT 2017. LNCS, vol. 10396, pp. 308–319. Springer, Cham (2017).  https://doi.org/10.1007/978-3-319-62809-7_23CrossRefGoogle Scholar
  12. 12.
    Průša, D.: Weight-reducing hennie machines and their descriptional complexity. In: Dediu, A.-H., Martín-Vide, C., Sierra-Rodríguez, J.-L., Truthe, B. (eds.) LATA 2014. LNCS, vol. 8370, pp. 553–564. Springer, Cham (2014).  https://doi.org/10.1007/978-3-319-04921-2_45CrossRefzbMATHGoogle Scholar
  13. 13.
    Shepherdson, J.C.: The reduction of two-way automata to one-way automata. IBM J. Res. Dev. 3(2), 198–200 (1959)MathSciNetCrossRefGoogle Scholar
  14. 14.
    Sipser, M.: Halting space-bounded computations. Theor. Comput. Sci. 10(3), 335–338 (1980)MathSciNetCrossRefGoogle Scholar
  15. 15.
    Tadaki, K., Yamakami, T., Lin, J.C.H.: Theory of one-tape linear-time Turing machines. Theor. Comput. Sci. 411(1), 22–43 (2010)MathSciNetCrossRefGoogle Scholar
  16. 16.
    Wagner, K.W., Wechsung, G.: Computational Complexity. D. Reidel Publishing Company, Dordrecht (1986)zbMATHGoogle Scholar

Copyright information

© IFIP International Federation for Information Processing 2018

Authors and Affiliations

  1. 1.Dipartimento di InformaticaUniversità degli Studi di MilanoMilanItaly

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