On the Size of Unary Probabilistic and Nondeterministic Automata


We investigate and compare the descriptional power of unary probabilistic and nondeterministic automata (pfa’s and nfa’s, respectively). We show the existence of a family of languages hard for pfa’s in the following sense: For any positive integer d, there exists a unary d-cyclic language such that any pfa accepting it requires d states, as the smallest deterministic automaton. On the other hand, we prove that there exist infinitely many languages having pfa’s which from one side do not match a known optimal state lower bound and, on the other side, they are smaller than nfa’s which, in turn, are smaller than deterministic automata.

DOI: 10.3233/FI-2011-583

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@article{Bianchi2011OnTS, title={On the Size of Unary Probabilistic and Nondeterministic Automata}, author={Maria Paola Bianchi and Carlo Mereghetti and Beatrice Palano and Giovanni Pighizzini}, journal={Fundam. Inform.}, year={2011}, volume={112}, pages={119-135} }