Unary Coded PSPACE-Complete Languages in ASPACE(loglog n)

  • Viliam Geffert
Part of the following topical collections:
  1. Computer Science Symposium in Russia


We study the class of binary coded versions of unary languages that can be accepted by alternating machines with loglog n space. We show that there exists a binary PSpace-complete language \(\mathcal {L}\) such that the unary coded version of \(\mathcal {L}\) is in ASpace(loglog n). Consequently, the standard translation between unary languages accepted with loglog n space and binary languages accepted with log n space works for alternating machines if and only ifP = PSpace. In general, if a binary language is accepted deterministically in 2 n nO(1) time and, simultaneously, in nO(1) space—which covers many PSpace-complete problems—then its unary coded version is accepted by an alternating Turing machine using an initially delimited worktape of size loglog n. This unexpected power follows from the fact that, with an auxiliary worktape of size O(loglog n) on a unary input 1 n , an alternating machine can simulate a stack with log n bits, representing the contents of the stack by its input head position. The standard push/pop operations on the stack are implemented by moving the head along the input.


Computational complexity Alternation Sublogarithmic space 



The author would like to thank the reviewers and the Program Committee of CSR 2017 for their suggestions, especially for sending a summary of PC discussions which gave inspiration for several improvements, and the anonymous reviewer of ToCS for helping to simplify the proof of Lemma 4.


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Authors and Affiliations

  1. 1.Department of Computer ScienceP. J. Šafárik UniversityKošiceSlovakia

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