The Minimum Amount of Useful Space: New Results and New Directions

  • Klaus Reinhardt
  • Abuzer Yakaryılmaz
Part of the Lecture Notes in Computer Science book series (LNCS, volume 8633)


We consider minimal space requirements when using memory with restricted access policy (pushdown - hence giving pushdown automata (PDAs), and counter - hence giving counter automata (CAs)) in connection with two-way and realtime head motion. The main results are that: (i) loglogn is a tight space lower bound for accepting general nonregular languages on weak realtime PDAs, (ii) there exist unary nonregular languages accepted by realtime alternating CAs within weak logn space, (iii) there exist nonregular languages accepted by two-way DPADs within strong loglogn space, and, (iv) there exist unary nonregular languages accepted by two-way CAs with quantum and classical states within middle logn space and bounded error.


Regular Language Quantum Register Input Tape Logarithmic Space Unary Language 
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Copyright information

© Springer International Publishing Switzerland 2014

Authors and Affiliations

  • Klaus Reinhardt
    • 1
    • 2
  • Abuzer Yakaryılmaz
    • 3
    • 4
  1. 1.Wilhelm-Schickard-Institut für InformatikUniversity of TübingenGermany
  2. 2.Humboldt University of BerlinGermany
  3. 3.Faculty of ComputingUniversity of LatviaRīgaLatvia
  4. 4.National Laboratory for Scientific ComputingPetrópolisBrazil

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