Unification modulo ACUI plus Homomorphisms/Distributivity
Identifieur interne : 005048 ( Hal/Curation ); précédent : 005047; suivant : 005049Unification modulo ACUI plus Homomorphisms/Distributivity
Auteurs : Siva Anantharaman [France] ; Paliath Narendran [France] ; Michaël Rusinowitch [France]Source :
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Abstract
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 `*' over `+', and prove it is NEXPTIME-decidable. When we assume the symbol `*' to be 2-sided distributive over `+', 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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<front><div type="abstract" xml:lang="en">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 `*' over `+', and prove it is NEXPTIME-decidable. When we assume the symbol `*' to be 2-sided distributive over `+', 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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<abstract xml:lang="en">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 `*' over `+', and prove it is NEXPTIME-decidable. When we assume the symbol `*' to be 2-sided distributive over `+', 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.</abstract>
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