Theory of Computing Systems

, Volume 55, Issue 2, pp 421–447 | Cite as

Two-Way Automata Versus Logarithmic Space

  • Christos A. Kapoutsis


We strengthen a previously known connection between the size complexity of two-way finite automata ( Open image in new window ) and the space complexity of Turing machines (tms). Specifically, we prove that
Here, Open image in new window and Open image in new window are the deterministic and nondeterministic Open image in new window , NL and L/poly are the standard classes of languages recognizable in logarithmic space by nondeterministic tms and by deterministic tms with access to polynomially long advice, and NLL and LL/polylog are the corresponding complexity classes for space O(loglogn) and advice length poly(logn). Our arguments strengthen and extend an old theorem by Berman and Lingas and can be used to obtain variants of the above statements for other modes of computation or other combinations of bounds for the input length, the space usage, and the length of advice.


Two-way finite automata 2D versus 2N Sakoda-Sipser conjecture Logarithmic space L versus NL Sub-logarithmic space 


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© Springer Science+Business Media New York 2013

Authors and Affiliations

  1. 1.LIAFAUniversité Paris Diderot—Paris VIIParis Cedex 13France

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