Finite automata for testing composition-based reconstructibility of sequences

Authors:
Qiang Li;Huimin Xie
Affiliations:
T-Life Research Center, Fudan University, Shanghai 200433, China;Department of Mathematics, Suzhou University, Suzhou 215006, China
Venue:
Journal of Computer and System Sciences
Year:
2008

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Abstract

Symbolic sequences uniquely reconstructible from all their substrings of length k compose a regular factorial language. We thoroughly characterize this language by its minimal forbidden words, and explicitly build up a deterministic finite automaton that accepts it. This provides an efficient on-line algorithm for testing the unique reconstructibility of the sequences.