Deciding unique decodability of bigram counts via finite automata

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 effi...

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Bibliographic Details
Published in:Journal of computer and system sciences Vol. 80; no. 2; pp. 450 - 456
Main Authors: Kontorovich, Aryeh, Trachtenberg, Ari
Format: Journal Article
Language:English
Published: Elsevier Inc 01.03.2014
Subjects:
Algorithms
Eulerian graph
Finite-state automata
Sequence reconstruction
Uniqueness
Sequence reconstruction
Eulerian graph
Finite-state automata
Uniqueness
ISSN:0022-0000, 1090-2724
Online Access:Get full text
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Summary: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. •We prove that the bigram-decodable strings form a regular language.•We construct a cubic-sized NFA for recognizing this language.•We show how to simulate this NFA efficiently.•We give a lower bound on the size of any DFA for this language.
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ISSN:0022-0000
1090-2724
DOI:10.1016/j.jcss.2013.09.003