eng
Schloss Dagstuhl – Leibniz-Zentrum für Informatik
Leibniz International Proceedings in Informatics
1868-8969
2023-08-21
17:1
17:15
10.4230/LIPIcs.MFCS.2023.17
article
Separating Automatic Relations
Barceló, Pablo
1
https://orcid.org/0000-0003-2293-2653
Figueira, Diego
2
https://orcid.org/0000-0003-0114-2257
Morvan, Rémi
2
https://orcid.org/0000-0002-1418-3405
Institute for Mathematical and Computational Engineering, Universidad Católica de Chile & CENIA & IMFD, Santiago, Chile
Univ. Bordeaux, CNRS, Bordeaux INP, LaBRI, UMR5800, F-33400 Talence, France
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.
https://drops.dagstuhl.de/storage/00lipics/lipics-vol272-mfcs2023/LIPIcs.MFCS.2023.17/LIPIcs.MFCS.2023.17.pdf
Automatic relations
recognizable relations
separability
finite colorability