State complexity of unique rational operations

For each basic language operation we define its “unique” counterpart as being the operation that results in a language whose words can be obtained uniquely through the given operation. These unique operations can arguably be viewed as combined basic operations, placing this work in the popular area of state complexity of combined operations on regular languages. We study the state complexity of unique rational operations and we provide upper bounds and empirical results meant to cast light into this matter. Equally important, we hope to have provided a generic methodology for estimating their state complexity.