Reconstructing Words from Right-Bounded-Block Words

📝 Original Info

• Title: Reconstructing Words from Right-Bounded-Block Words
• ArXiv ID: 2001.11218
• Date: 2020-03-17
• Authors: Pamela Fleischmann, Marie Lejeune, Florin Manea, Dirk Nowotka, Michel Rigo

📝 Abstract

A reconstruction problem of words from scattered factors asks for the minimal information, like multisets of scattered factors of a given length or the number of occurrences of scattered factors from a given set, necessary to uniquely determine a word. We show that a word $w \in \{a, b\}^{*}$ can be reconstructed from the number of occurrences of at most $\min(|w|_a, |w|_b)+ 1$ scattered factors of the form $a^{i} b$. Moreover, we generalize the result to alphabets of the form $\{1,\ldots,q\}$ by showing that at most $ \sum^{q-1}_{i=1} |w|_i (q-i+1)$ scattered factors suffices to reconstruct $w$. Both results improve on the upper bounds known so far. Complexity time bounds on reconstruction algorithms are also considered here.

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