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.
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Kapoutsis, C.A., Lefebvre, N. (2012). Analogs of Fagin’s Theorem for Small Nondeterministic Finite Automata. In: Yen, HC., Ibarra, O.H. (eds) Developments in Language Theory. DLT 2012. Lecture Notes in Computer Science, vol 7410. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-31653-1_19
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DOI: https://doi.org/10.1007/978-3-642-31653-1_19
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