Unique decodability of bigram counts by finite automata
Aryeh Kontorovich, Ari Trachtenberg · arXiv (Cornell University) · 2011
We revisit the problem of deciding whether a given string is uniquely decodable from its bigram counts by means of a finite automaton. An efficient algorithm for constructing a polynomial-size nondeterministic finite automaton that decides unique decodability is given. Conversely, we show that the minimum deterministic finite automaton for deciding unique decodability has at least exponentially many states in alphabet size.