Analogs of Fagin’s Theorem for Small Nondeterministic Finite Automata
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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- 2.Blum, L., Cucker, F., Shub, M., Smale, S.: Complexity and real computation. Springer (1997)Google Scholar
- 4.Fagin, R.: Generalized first-order spectra and polynomial-time recognizable sets. In: Karp, R.M. (ed.) Complexity of Computation. AMS-SIAM Symposia in Applied Mathematics, vol. VII, pp. 43–73 (1974)Google Scholar
- 5.Immerman, N.: Descriptive complexity. Springer (1998)Google Scholar
- 8.Papadimitriou, C.H.: Computational complexity. Addison-Wesley (1994)Google Scholar
- 10.Sakoda, W.J., Sipser, M.: Nondeterminism and the size of two-way finite automata. In: Proceedings of STOC, pp. 275–286 (1978)Google Scholar