InforLorV4, Hal, Curation, bibRecord, 005048

Unification modulo ACUI plus Homomorphisms/Distributivity

Identifieur interne : 005048 ( Hal/Curation ); précédent : 005047; suivant : 005049

Unification modulo ACUI plus Homomorphisms/Distributivity

Auteurs : Siva Anantharaman [France] ; Paliath Narendran [France] ; Michaël Rusinowitch [France]

Source :

RBID : Hal:hal-00080670

English descriptors

mix :
- E-Unification, Minsky machine, Post correspondence problem, complexity, rewrite reachability, set constraints.

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.

Url:

https://hal.archives-ouvertes.fr/hal-00080670

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Le document en format XML

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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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<notesStmt><note type="commentary">19th International Conference on Automated Deduction, Miami Beach, FL, USA, July 28 – August 2, 2003, Proceedings</note>
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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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   |type=    RBID
   |clé=     Hal:hal-00080670
   |texte=   Unification modulo ACUI plus Homomorphisms/Distributivity
}}

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Unification modulo ACUI plus Homomorphisms/Distributivity

Unification modulo ACUI plus Homomorphisms/Distributivity

Source :

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Abstract

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