Strong optimal lower bounds for Turing machines that accept nonregular languages

  • Alberto Bertoni
  • Carlo Mereghetti
  • Giovanni Pighizzini
Contributed Papers Lower Bounds
Part of the Lecture Notes in Computer Science book series (LNCS, volume 969)


In this paper, simultaneous lower bounds on space and input head reversals for deterministic, nondeterministic and alternating Turing machines accepting nonregular languages are studied.

Three notions of space complexity, namely strong, middle, and weak, are considered; moreover, another notion called accept, is introduced. For all cases we obtain tight lower bounds. In particular, we prove that while in the deterministic and nondeterministic case these bounds are “strongly” optimal—in the sense that we exhibit a nonregular language over a unary alphabet exactly fitting them—in the alternating case optimal lower bounds for tally languages turn out to be higher than those for arbitrary languages.


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Copyright information

© Springer-Verlag Berlin Heidelberg 1995

Authors and Affiliations

  • Alberto Bertoni
    • 1
  • Carlo Mereghetti
    • 1
  • Giovanni Pighizzini
    • 1
  1. 1.Dipartimento di Scienze dell'InformazioneUniversitá degli Studi di MilanoMilanoItaly

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