Reconstructing Words from Right-Bounded-Block Words
share
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 ∈{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,...,q} by showing that at most ∑^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.
READ FULL TEXT