Weighted Automata Computation of Edit Distances with Consolidations and Fragmentations

Mathieu Giraud (1, 2) , Florent Jacquemard (3, 4)

1 CRIStAL - Centre de Recherche en Informatique, Signal et Automatique de Lille - UMR 9189
2 Algomus
3 Inria de Paris
4 CEDRIC - VERTIGO - CEDRIC. Données complexes, apprentissage et représentations

We study edit distances between strings, based on operations of character substitutions, insertions, deletions and additionally consolidations and fragmentations. The two latter operations transform a sequence of characters into one character and vice-versa. They correspond to the compression and expansion in Dynamic Time-Warping algorithms for speech recognition and are also used for the formal analysis of written music. Such edit distances are not computable in general for arbitrary rulesets. We propose weighted automaton constructions to compute an edit distance taking into account both consolidations and deletions, or both fragmentations and insertions. Assuming that the operation ruleset has a constant size, these constructions are polynomial into the lengths of the involved strings. We finally show that the optimal weight of sequences made of consolidations chained with fragmentations, in that order, is computable for arbitrary rulesets, and not computable if we reverse the order of fragmentations and consolidations.

Mots clés: Edit Distance; Edit Operation; Weighted Automata; Consolidation; Bounded Semiring; Fragmentation

Domaines: Théorie et langage formel [cs.FL]; Algorithme et structure de données [cs.DS]; Bio-informatique [q-bio.QM]; Musique, musicologie et arts de la scène

Mathieu Giraud, Florent Jacquemard. Weighted Automata Computation of Edit Distances with Consolidations and Fragmentations. Information and Computation, 2022, 282, pp.104652. ⟨10.1016/j.ic.2020.104652⟩. ⟨hal-01857267v4⟩