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On the Size of Unary Probabilistic and Nondeterministic Automata

Bianchi M.P., Mereghetti C., Palano B., Pighizzini G.

Fundamenta Informaticae

2011

Vol. 112, nr 2/3

119-135

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.