Sequence Decision Diagrams

Compact encoding of finite sets of strings is a classic problem. Themanipulation of large sets requires compact data structures that allow for efficient set operations. We define sequence decision diagrams (SeqDDs), which can encode arbitrary finite sets of strings over an alphabet. SeqDDs can be seen as a variant of classic decision diagrams such as BDDs and MDDs where, instead of a fixed number of levels, we simply require that the number of paths and the lengths of these paths be finite. However, the main difference between the two is the target application: while MDDs are suited to store and manipulate large sets of constant-length tuples, SeqDDs can store arbitrary finite languages and, as such, should be studied in relation to finite automata. We do so, examining in particular the size of equivalent representations.