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/poly ⊇ NL 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 ⊉ NL. © 2012 Springer-Verlag.
CITATION STYLE
Kapoutsis, C. A., & Pighizzini, G. (2012). Two-way automata characterizations of L/poly versus NL. In Lecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics) (Vol. 7353 LNCS, pp. 217–228). https://doi.org/10.1007/978-3-642-30642-6_21
Mendeley helps you to discover research relevant for your work.