Incomplete transition complexity of some basic operations

Abstract

Y. Gao et al. studied for the first time the transition complexity of Boolean operations on regular languages based on not necessarily complete DFAs. For the intersection and the complementation, tight bounds were presented, but for the union operation the upper and lower bounds differ by a factor of two. In this paper we continue this study by giving tight upper bounds for the concatenation, the Kleene star and the reversal operations. We also give a new tight upper bound for the transition complexity of the union, which refutes the conjecture presented by Y. Gao, et al. © 2013 Springer-Verlag Berlin Heidelberg.