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Linear-Time Limited Automata

  • Bruno Guillon
  • Luca Prigioniero
Conference paper
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.

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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