Enumeration of MSO Queries on Strings with Constant Delay and Logarithmic Updates

We consider the enumeration of MSO queries over strings under updates. For each MSO query we build an index structure enjoying the following properties: The index structure can be constructed in linear time, it can be updated in logarithmic time and it allows for constant delay time enumeration. This improves from the previous known index structures allowing for constant delay enumeration that would need to be reconstructed from scratch, hence in linear time, in the presence of updates. We allow relabeling updates, insertion of individual labels and removal of individual labels.