Unification Modulo ACUI Plus Distributivity Axioms
Identifieur interne : 006B10 ( Main/Exploration ); précédent : 006B09; suivant : 006B11Unification Modulo ACUI Plus Distributivity Axioms
Auteurs : Siva Anantharaman [France] ; Paliath Narendran [États-Unis] ; Michael Rusinowitch [France]Source :
- Journal of Automated Reasoning [ 0168-7433 ] ; 2004-07-01.
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Abstract
Abstract: E-unification problems are central in automated deduction. In this work, we consider unification modulo theories that extend the well-known ACI or ACUI by adding a binary symbol “*” that distributes over the AC(U)I-symbol “+.” If this distributivity is one-sided (say, to the left), we get the theory denoted AC(U)IDl; we show that AC(U)IDl-unification is DEXPTIME-complete. If “*” is assumed two-sided distributive over “+,” we get the theory denoted AC(U)ID; we show unification modulo AC(U)ID to be NEXPTIME-decidable and DEXPTIME-hard. Both AC(U)IDl and AC(U)ID seem to be of practical interest, for example, in the analysis of programs modeled in terms of process algebras. Our results, for the two theories considered, are obtained through two entirely different lines of reasoning. A consequence of our methods of proof is that, modulo the theory that adds to AC(U)ID the assumption that “*” is associative-commutative, or just associative, unification is undecidable.
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DOI: 10.1007/s10817-004-2279-7
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ident="en">en</language></langUsage></profileDesc></teiHeader><front><div type="abstract" xml:lang="en">Abstract: E-unification problems are central in automated deduction. In this work, we consider unification modulo theories that extend the well-known ACI or ACUI by adding a binary symbol “*” that distributes over the AC(U)I-symbol “+.” If this distributivity is one-sided (say, to the left), we get the theory denoted AC(U)IDl; we show that AC(U)IDl-unification is DEXPTIME-complete. If “*” is assumed two-sided distributive over “+,” we get the theory denoted AC(U)ID; we show unification modulo AC(U)ID to be NEXPTIME-decidable and DEXPTIME-hard. Both AC(U)IDl and AC(U)ID seem to be of practical interest, for example, in the analysis of programs modeled in terms of process algebras. Our results, for the two theories considered, are obtained through two entirely different lines of reasoning. A consequence of our methods of proof is that, modulo the theory that adds to AC(U)ID the assumption that “*” is associative-commutative, or just associative, unification is undecidable.</div></front></TEI><affiliations><list><country><li>France</li><li>États-Unis</li></country><region><li>Centre-Val de Loire</li><li>Grand Est</li><li>Lorraine (région)</li><li>Région Centre</li></region><settlement><li>Nancy</li><li>Orléans</li></settlement></list><tree><country name="France"><region name="Centre-Val de Loire"><name sortKey="Anantharaman, Siva" sort="Anantharaman, Siva" uniqKey="Anantharaman S" first="Siva" last="Anantharaman">Siva Anantharaman</name></region><name sortKey="Anantharaman, Siva" sort="Anantharaman, Siva" uniqKey="Anantharaman S" first="Siva" last="Anantharaman">Siva Anantharaman</name><name sortKey="Rusinowitch, Michael" sort="Rusinowitch, Michael" uniqKey="Rusinowitch M" first="Michael" last="Rusinowitch">Michael Rusinowitch</name><name sortKey="Rusinowitch, Michael" sort="Rusinowitch, Michael" uniqKey="Rusinowitch M" first="Michael" last="Rusinowitch">Michael Rusinowitch</name></country><country name="États-Unis"><noRegion><name sortKey="Narendran, Paliath" sort="Narendran, Paliath" uniqKey="Narendran P" first="Paliath" last="Narendran">Paliath Narendran</name></noRegion><name sortKey="Narendran, Paliath" sort="Narendran, Paliath" uniqKey="Narendran P" first="Paliath" last="Narendran">Paliath Narendran</name></country></tree></affiliations></record>Pour manipuler ce document sous Unix (Dilib)
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