Deciding unique decodability of bigram counts via finite automata

Aryeh Kontorovich, Ari Trachtenberg

Research output: Contribution to journalArticlepeer-review

2 Scopus citations


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.

Original languageEnglish
Pages (from-to)450-456
Number of pages7
JournalJournal of Computer and System Sciences
Issue number2
StatePublished - 1 Jan 2014


  • Eulerian graph
  • Finite-state automata
  • Sequence reconstruction
  • Uniqueness

ASJC Scopus subject areas

  • Theoretical Computer Science
  • General Computer Science
  • Computer Networks and Communications
  • Computational Theory and Mathematics
  • Applied Mathematics


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