Two-Way Automata Characterizations of L/poly versus NL

  • Christos A. Kapoutsis
  • Giovanni Pighizzini
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7353)


Let L/poly and NL be the standard complexity classes, of languages recognizable in logarithmic space by Turing machines which are deterministic with polynomially-long advice and nondeterministic without advice, respectively. We recast the question whether L/polyNL in terms of deterministic and nondeterministic two-way finite automata (2dfas and 2nfas). We prove it equivalent to the question whether every s-state unary 2nfa has an equivalent poly(s)-state 2dfa, or whether a poly(h)-state 2dfa, can check accessibility in h-vertex graphs (even under unary encoding) or check two-way liveness in h-tall, h-column graphs. This complements two recent improvements of an old theorem of Berman and Lingas. On the way, we introduce new types of reductions between regular languages (even unary ones), use them to prove the completeness of specific languages for two-way nondeterministic polynomial size, and propose a purely combinatorial conjecture that implies L/poly \(\nsupseteq\) NL.


Prime Power Regular Language Logarithmic Space Nondeterministic Choice Output Tape 
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Copyright information

© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Christos A. Kapoutsis
    • 1
  • Giovanni Pighizzini
    • 2
  1. 1.LIAFAUniversité Paris VIIFrance
  2. 2.DICoUniversità degli Studi di MilanoItalia

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