Analogs of Fagin’s Theorem for Small Nondeterministic Finite Automata

  • Christos A. Kapoutsis
  • Nans Lefebvre
Part of the Lecture Notes in Computer Science book series (LNCS, volume 7410)


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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© Springer-Verlag Berlin Heidelberg 2012

Authors and Affiliations

  • Christos A. Kapoutsis
    • 1
  • Nans Lefebvre
    • 1
  1. 1.LIAFA, Université Paris VIIFrance

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