Analogs of fagin's theorem for small nondeterministic finite automata

Authors:
Christos A. Kapoutsis;Nans Lefebvre
Affiliations:
LIAFA, Université Paris VII, France;LIAFA, Université Paris VII, France
Venue:
DLT'12 Proceedings of the 16th international conference on Developments in Language Theory
Year:
2012

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Abstract

Let 1N and SN be the classes of families of problems solvable by families of polynomial-size one-way and sweeping nondeterministic finite automata, respectively. We characterize 1N in terms of families of polynomial-length formulas of monadic second-order logic with successor. These formulas existentially quantify two local conditions in disjunctive normal form: one on cells polynomially away from the two ends of the input, and one more on the cells of a fixed-width window sliding along it. We then repeat the same for SN and for slightly more complex formulas.