One Idea

There is a compact data structure for words: automata. Finite automata can “store” many words, even infinitely many—in the sense that the language of a finite automaton can be infinite. This powerful feature makes automata ubiquitous in computer science. Lecture notes by Javier Esparza emphasize this view of automata as data structures. The most fundamental algorithmic problems on automata are: operations, such as computing set union or complement of the languages of automata; tests, such as checking their languages for equality. In this post I focus on the latter: equivalence checking. In general, equivalence checking for automata is PSPACE-complete, which is excusable considering how compact and flexible data structures they are. One can check two deterministic finite automata for equivalence in polynomial time, by searching their product. Less known is the fact that one can efficiently check much wider classes of automata for equivalence, including unambiguous auto...