Nondeterminism and succinctly representable regular languages
SAICSIT '02 Proceedings of the 2002 annual research conference of the South African institute of computer scientists and information technologists on Enablement through technology
Random Number Generation with +-NFAs
CIAA '01 Revised Papers from the 6th International Conference on Implementation and Application of Automata
A family of NFAs which need 2n - α deterministic states
Theoretical Computer Science
| Hi-index | 0.00 |
Iwama et al [1] showed that there exists an n-state binary nondeterministic finite automaton such that its equivalent minimal deterministic finite automaton has exactly 2n– α states, for all n ≥ 7 and 5 ≤ α ≤ 2n – 2, subject to certain coprimality conditions. We investigate the same question for both unary and binary symmetric difference nondeterministic finite automata [2]. In the binary case, we show that for any n ≥ 4, there is an n-state ⊕-NFA which needs 2n−−1 + 2k−−1 –1 states, for 2k ≤ n – 1. In the unary case, we prove the following result for a large practical subclass of unary symmetric difference nondeterministic finite automata: For all n ≥ 2, we show that there are many values of α such that there is no n-state unary symmetric difference nondeterministic finite automaton with an equivalent deterministic finite automaton with 2n – α states, where 0 αn−1. For each n ≥ 2, we quantify such values of α precisely.