A Possibilistic Distance for Sequences of Equal and Unequal Length

Abstract

We generalize Hamming distances to sequences of possibilistic letters: this corresponds to passing from ordinary binary logics to an infinite-valued logical setting. Our proposal is validated on a possibilistic model of a noisy communication channel, as opposed to the random-noise models which are current in information theory; it might prove to be a basis for “soft decoding” of noisy data. We take into account both synchronous and non-synchronous channels; the latter require a further generalization to sequences of unequal length in the spirit of Levenštejn distance; by so doing, we re-take a problem which Prof. Solomon Marcus had suggested to the second author when both were even younger than they are nowadays.