Operations on Unambiguous Finite Automata

Abstract

A nondeterministic finite automaton is unambiguous if it has at most one accepting computation on every input string. We investigate the complexity of basic regular operations on languages represented by unambiguous finite automata. We get tight upper bounds for intersection (mn), left and right quotients ($2^n-1$), positive closure (${3\over 4}\cdot 2^n-1$), star (${3\over 4}\cdot 2^n$), shuffle ($2^{mn}-1$), and concatenation (${3\over 4}\cdot 2^{m+n}-1$). To prove tightness, we use a binary alphabet for intersection and left and right quotients, a ternary alphabet for star and positive closure, a five-letter alphabet for shuffle, and a seven-letter alphabet for concatenation. We also get some partial results for union and complementation.

G. Jirásková—Research supported by VEGA grant 2/0084/15 and grant APVV-15-0091.

J. Šebej—Research supported by VEGA grant 1/0142/15 and grant APVV-15-0091.