In many applications, faults are triggered by events that occur in a particular order. In fact, many bugs are caused by the interaction of only a low number of such events. Based on this assumption, sequence covering arrays (SCAs) have recently been proposed as suitable designs for event sequence testing. In practice, directly applying SCAs for testing is often impaired by additional constraints, and SCAs have to be adapted to fit application-specific needs. Modifying precomputed SCAs to account for problem variations can be problematic, if not impossible, and developing dedicated algorithms is costly. In this article, we propose answer-set programming (ASP), a well-known knowledge-representation formalism from the area of artificial intelligence based on logic programming, as a declarative paradigm for computing SCAs. Our approach allows to concisely state complex coverage criteria in an elaboration tolerant way, i.e., small variations of a problem specification require only small modifications of the ASP representation. Employing ASP for computing SCAs is further justified by new complexity results related to event-sequence testing that are established in this work.