an:06028490
Zbl 1236.68168
Geffert, Viliam; Pighizzini, Giovanni
Pairs of complementary unary languages with ``balanced'' nondeterministic automata
EN
Algorithmica 63, No. 3, 571-587 (2012).
00297227
2012
j
68Q45
finite state automata; state complexity; unary regular languages; unary automata
Summary: For each sufficiently large \(n\), there exists a unary regular language \(L\) such that both \(L\) and its complement \(L ^{c}\) are accepted by unambiguous nondeterministic automata with at most \(n\) states, while the smallest deterministic automata for these two languages still require a superpolynomial number of states, at least \(e^{\Omega(\root 3 \of {n\cdot\ln^{2}n})}\). Actually, \(L\) and \(L ^{c}\) are ``balanced'' not only in the number of states but, moreover, they are accepted by nondeterministic machines sharing the same transition graph, differing only in the distribution of their final states. As a consequence, the gap between the sizes of unary unambiguous self-verifying automata and deterministic automata is also superpolynomial.