A Lattice of Sets of Alignments Built on the Common Subword in a Finite Language

Laurent Miclet (1) , Nelly Barbot (2) , Baptiste Jeudy (3)

1 Dyliss - Dynamics, Logics and Inference for biological Systems and Sequences
2 CORDIAL - Human-machine spoken dialogue
3 LHC - Laboratoire Hubert Curien

We define the locally maximal subwords and locally minimal superwords common to a finite set of words. We also define the corresponding sets of alignments. We give a partial order relation between such sets of alignments, as well as two operations between them. We show that the constructed family of sets of alignments has the lattice structure. We give hints to use this structure as a machine learning basis for inducing a generalization of the set of words.

Mots clés: Finite languages; locally maximal subwords; alignments; algebraic structure of sets of alignments on a set of words; lattice; machine learning; learning by analogy

Domaines: Apprentissage [cs.LG]; Théorie et langage formel [cs.FL]

Laurent Miclet, Nelly Barbot, Baptiste Jeudy. A Lattice of Sets of Alignments Built on the Common Subword in a Finite Language. International Conference on Grammatical Inference, Sep 2012, United States. pp.164-176. ⟨hal-00726166⟩