Abstract
The aim of this paper is to give two new logical characterizations of NLIN (nondeterministic linear time) improving significantly a previous characterization of E. Grandjean (1994, SIAM J. Comput. 23 , 573–597; and F. Olive, 1998, Comput. Complexity 7 , 54–97). It is known that NLIN coincides with the class of problems definable by formulas of the prenex form ∃ f 1 …∃ f k ϕ where the f i are unary function symbols and ϕ is first-order, prenex, with only one universal quantifier. We show that the characterization remains true in the two following cases: (a) Unary functions are replaced by a single binary relation whose outdegree is bounded by some fixed constant h . (b) When only ordered structures are considered, unary functions are restricted to be bijective.
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