# Unification modulo ACUI plus Homomorphisms/Distributivity

3 CASSIS - Combination of approaches to the security of infinite states systems
FEMTO-ST - Franche-Comté Électronique Mécanique, Thermique et Optique - Sciences et Technologies (UMR 6174), INRIA Lorraine, LORIA - Laboratoire Lorrain de Recherche en Informatique et ses Applications
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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Conference papers

https://hal.archives-ouvertes.fr/hal-00080670
Contributor : Siva Anantharaman <>
Submitted on : Tuesday, June 20, 2006 - 9:47:05 AM
Last modification on : Thursday, June 27, 2019 - 1:24:45 AM

### Identifiers

• HAL Id : hal-00080670, version 1

### Citation

Siva Anantharaman, Paliath Narendran, Michaël Rusinowitch. Unification modulo ACUI plus Homomorphisms/Distributivity. 2003, pp.442--457. ⟨hal-00080670⟩

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