Constrained Many-to-One String Editing with Memory

A new constrained edit distance between an ordered set of input strings and a single output string is proposed. All the strings are assumed to have finite lengths and to be over a finite alphabet. Editing transformation respectively includes deletion of symbols from the input strings, combination of the so-reduced input strings by a function with memory, and substitution and insertion of symbols in the combination string. Constraints are related to the total number of edit operations and to the maximum number of consecutive deletions and insertions. A recursive algorithm for efficient computation of the constrained edit distance is derived and its computational complexity is determined. Potential applications in cryptanalysis of shift register based stream ciphers and in decoding for parallel communication channels with synchronization errors are also discussed.