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Communication Dans Un Congrès Année : 2023

Separating Automatic Relations

Résumé

We study the separability problem for automatic relations (i.e., relations on finite words definable by synchronous automata) in terms of recognizable relations (i.e., finite unions of products of regular languages). This problem takes as input two automatic relations R and R', and asks if there exists a recognizable relation S that contains R and does not intersect R'. We show this problem to be undecidable when the number of products allowed in the recognizable relation is fixed. In particular, checking if there exists a recognizable relation S with at most k products of regular languages that separates R from R' is undecidable, for each fixed k ≥ 2. Our proofs reveal tight connections, of independent interest, between the separability problem and the finite coloring problem for automatic graphs, where colors are regular languages.

Dates et versions

hal-04099907 , version 1 (17-05-2023)

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Pablo Barceló, Diego Figueira, Rémi Morvan. Separating Automatic Relations. International Symposium on Mathematical Foundations of Computer Science (MFCS), Aug 2023, Bordeaux, France. ⟨hal-04099907⟩

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