Unification modulo ACUI plus homomorphisms/distributivity
Identifieur interne : 007F23 ( Main/Merge ); précédent : 007F22; suivant : 007F24Unification 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.
Descripteurs français
- Pascal (Inist)
English descriptors
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 ACUIDl-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:04-0200275Le 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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