Deciding unique decodability of bigram counts via finite automata

Authors:
Aryeh Kontorovich;Ari Trachtenberg
Affiliations:
Department of Computer Science, Ben-Gurion University, Beer Sheva 84105, Israel;Department of Electrical & Computer Engineering, Boston University, 8 Saint Marys Street, Boston, MA 02215, United States
Venue:
Journal of Computer and System Sciences
Year:
2014

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Abstract

We revisit the problem of deciding by means of a finite automaton whether a string is uniquely decodable from its bigram counts. An efficient algorithm for constructing a polynomial-size Nondeterministic Finite Automaton (NFA) that decides unique decodability is given. This NFA may be simulated efficiently in time and space. Conversely, we show that the minimum deterministic finite automaton for deciding unique decodability has exponentially many states in alphabet size, and compute the correct order of magnitude of the exponent.