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Unification modulo ACUI plus homomorphisms/distributivity

Identifieur interne : 007F23 ( Main/Merge ); précédent : 007F22; suivant : 007F24

Unification modulo ACUI plus homomorphisms/distributivity

Auteurs : Siva Anantharaman [France] ; Paliath Narendran [États-Unis] ; Michael Rusinowitch [France]

Source :

Lecture notes in computer science [ 0302-9743 ] ; 2003.

RBID : Pascal:04-0200275

Descripteurs français

Pascal (Inist)
- Démonstration automatique, Unification, Homomorphisme, Décidabilité, Commutativité, Associativité.

English descriptors

KwdEn :
- Associativity, Automatic proving, Commutativity, Decidability, Homomorphism, Unification.

Abstract

In this paper, we consider the unification problem over theories that are extensions of ACI or ACUI, obtained by adding finitely many homomorphism symbols, or a symbol '*' that distributes over the ACUI-symbol denoted '+'. We first show that when we adjoin a set of commuting homomorphisms to ACUI, unification is undecidable. We then consider the ACUID_l-unification problem, i.e., unification modulo ACUI plus left-distributivity of a given '*' w.r.t. '+', and prove its NEXPTIME-decidability. When we assume the symbol '*' to be 2-sided distributive w.r.t. '+', we get the theory ACUID, for which the unification problem remains decidable. But when equations of associativity-commutativity, or just of associativity, on '*' are added on to ACUID, the unification problem becomes undecidable.

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Pascal:04-0200275

Le document en format XML

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<front><div type="abstract" xml:lang="en">In this paper, we consider the unification problem over theories that are extensions of ACI or ACUI, obtained by adding finitely many homomorphism symbols, or a symbol '*' that distributes over the ACUI-symbol denoted '+'. We first show that when we adjoin a set of commuting homomorphisms to ACUI, unification is undecidable. We then consider the ACUID<sub>l</sub>
-unification problem, i.e., unification modulo ACUI plus left-distributivity of a given '*' w.r.t. '+', and prove its NEXPTIME-decidability. When we assume the symbol '*' to be 2-sided distributive w.r.t. '+', we get the theory ACUID, for which the unification problem remains decidable. But when equations of associativity-commutativity, or just of associativity, on '*' are added on to ACUID, the unification problem becomes undecidable.</div>
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Unification modulo ACUI plus homomorphisms/distributivity

Unification modulo ACUI plus homomorphisms/distributivity

Source :

Descripteurs français

English descriptors

Abstract

Links toward previous steps (curation, corpus...)

Links to Exploration step

Le document en format XML

Pour manipuler ce document sous Unix (Dilib)

Pour mettre un lien sur cette page dans le réseau Wicri