The equational theory of the natural join and inner union is decidable

Abstract : The natural join and the inner union operations combine relations of a database. Tropashko and Spight [24] realized that these two operations are the meet and join operations in a class of lattices, known by now as the relational lattices. They proposed then lattice theory as an algebraic approach to the theory of databases, alternative to the relational algebra. Previous works [17, 22] proved that the quasiequational theory of these lattices—that is, the set of definite Horn sentences valid in all the relational lattices—is undecidable, even when the signature is restricted to the pure lattice signature. We prove here that the equational theory of relational lattices is decidable. That, is we provide an algorithm to decide if two lattice theoretic terms t, s are made equal under all intepretations in some relational lattice. We achieve this goal by showing that if an inclusion t ≤ s fails in any of these lattices, then it fails in a relational lattice whose size is bound by a triple exponential function of the sizes of t and s.
Type de document :
Communication dans un congrès
Springer. FOSSACS 2018, Apr 2018, Thessaloniki, Greece. 10803, pp.494--510, 2018, Foundations of Software Science and Computation Structures - 21st International Conference, FOSSACS 2018, Held as Part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2018, Thessaloniki, Greece, April 14-20, 2018, Proceedings. 〈10.1007/978-3-319-89366-2_27〉
Liste complète des métadonnées

Littérature citée [24 références]  Voir  Masquer  Télécharger

https://hal.archives-ouvertes.fr/hal-01625134
Contributeur : Luigi Santocanale <>
Soumis le : vendredi 27 octobre 2017 - 12:59:02
Dernière modification le : lundi 4 mars 2019 - 14:04:14
Document(s) archivé(s) le : dimanche 28 janvier 2018 - 13:00:53

Fichiers

0.pdf
Fichiers produits par l'(les) auteur(s)

Identifiants

Collections

Citation

Luigi Santocanale. The equational theory of the natural join and inner union is decidable. Springer. FOSSACS 2018, Apr 2018, Thessaloniki, Greece. 10803, pp.494--510, 2018, Foundations of Software Science and Computation Structures - 21st International Conference, FOSSACS 2018, Held as Part of the European Joint Conferences on Theory and Practice of Software, ETAPS 2018, Thessaloniki, Greece, April 14-20, 2018, Proceedings. 〈10.1007/978-3-319-89366-2_27〉. 〈hal-01625134〉

Partager

Métriques

Consultations de la notice

420

Téléchargements de fichiers

47