On superposition-based satisfiability procedures and their combination
Identifieur interne :
000536 ( PascalFrancis/Curation );
précédent :
000535;
suivant :
000537
On superposition-based satisfiability procedures and their combination
Auteurs : Hélène Kirchner [
France] ;
Silvio Ranise [
France] ;
Christophe Ringeissen [
France] ;
DUC KHANH TRAN [
France]
Source :
-
Lecture notes in computer science [ 0302-9743 ] ; 2005.
RBID : Pascal:05-0479611
Descripteurs français
English descriptors
Abstract
We study how to efficiently combine satisfiability procedures built by using a superposition calculus with satisfiability procedures for theories, for which the superposition calculus may not apply (e.g., for various decidable fragments of Arithmetic). Our starting point is the Nelson-Oppen combination method, where satisfiability procedures cooperate by exchanging entailed (disjunction of) equalities between variables. We show that the superposition calculus deduces sufficiently many such equalities for convex theories (e.g., the theory of equality and the theory of lists) and disjunction of equalities for non-convex theories (e.g., the theory of arrays) to guarantee the completeness of the combination method. Experimental results on proof obligations extracted from the certification of auto-generated aerospace software confirm the efficiency of the approach. Finally, we show how to make satisfiability procedures built by superposition both incremental and resettable by using a hierarchic variant of the Nelson-Oppen method.
| pA |
| A01 | 01 | 1 | | @0 0302-9743 |
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| A05 | | | | @2 3722 |
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| A08 | 01 | 1 | ENG | @1 On superposition-based satisfiability procedures and their combination |
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| A09 | 01 | 1 | ENG | @1 Theoretical aspects of computing - ICTAC 2005 : Second international colloquium, Hanoi, Vietnam, October 17-21, 2005, proceedings |
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| A11 | 01 | 1 | | @1 KIRCHNER (Hélène) |
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| A11 | 02 | 1 | | @1 RANISE (Silvio) |
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| A11 | 03 | 1 | | @1 RINGEISSEN (Christophe) |
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| A11 | 04 | 1 | | @1 DUC KHANH TRAN |
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| A14 | 01 | | | @1 LORIA & INRIA-Lorraine @3 FRA @Z 1 aut. @Z 2 aut. @Z 3 aut. @Z 4 aut. |
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| A20 | | | | @1 594-608 |
|---|
| A21 | | | | @1 2005 |
|---|
| A23 | 01 | | | @0 ENG |
|---|
| A26 | 01 | | | @0 3-540-29107-5 |
|---|
| A43 | 01 | | | @1 INIST @2 16343 @5 354000124518530390 |
|---|
| A44 | | | | @0 0000 @1 © 2005 INIST-CNRS. All rights reserved. |
|---|
| A45 | | | | @0 16 ref. |
|---|
| A47 | 01 | 1 | | @0 05-0479611 |
|---|
| A60 | | | | @1 P @2 C |
|---|
| A61 | | | | @0 A |
|---|
| A64 | 01 | 1 | | @0 Lecture notes in computer science |
|---|
| A66 | 01 | | | @0 USA |
|---|
| C01 | 01 | | ENG | @0 We study how to efficiently combine satisfiability procedures built by using a superposition calculus with satisfiability procedures for theories, for which the superposition calculus may not apply (e.g., for various decidable fragments of Arithmetic). Our starting point is the Nelson-Oppen combination method, where satisfiability procedures cooperate by exchanging entailed (disjunction of) equalities between variables. We show that the superposition calculus deduces sufficiently many such equalities for convex theories (e.g., the theory of equality and the theory of lists) and disjunction of equalities for non-convex theories (e.g., the theory of arrays) to guarantee the completeness of the combination method. Experimental results on proof obligations extracted from the certification of auto-generated aerospace software confirm the efficiency of the approach. Finally, we show how to make satisfiability procedures built by superposition both incremental and resettable by using a hierarchic variant of the Nelson-Oppen method. |
|---|
| C02 | 01 | X | | @0 001D02A05 |
|---|
| C03 | 01 | X | FRE | @0 Décidabilité @5 06 |
|---|
| C03 | 01 | X | ENG | @0 Decidability @5 06 |
|---|
| C03 | 01 | X | SPA | @0 Decidibilidad @5 06 |
|---|
| C03 | 02 | X | FRE | @0 Traitement liste @5 07 |
|---|
| C03 | 02 | X | ENG | @0 List processing @5 07 |
|---|
| C03 | 02 | X | SPA | @0 Tratamiento lista @5 07 |
|---|
| C03 | 03 | X | FRE | @0 Superposition @5 18 |
|---|
| C03 | 03 | X | ENG | @0 Superposition @5 18 |
|---|
| C03 | 03 | X | SPA | @0 Superposición @5 18 |
|---|
| C03 | 04 | X | FRE | @0 Satisfiabilité @5 19 |
|---|
| C03 | 04 | X | ENG | @0 Satisfiability @5 19 |
|---|
| C03 | 04 | X | SPA | @0 Satisfactibilidad @5 19 |
|---|
| C03 | 05 | X | FRE | @0 Disjonction @5 20 |
|---|
| C03 | 05 | X | ENG | @0 Disjunction @5 20 |
|---|
| C03 | 05 | X | SPA | @0 Disyunción @5 20 |
|---|
| C03 | 06 | X | FRE | @0 Certification @5 21 |
|---|
| C03 | 06 | X | ENG | @0 Certification @5 21 |
|---|
| C03 | 06 | X | SPA | @0 Certificación @5 21 |
|---|
| C03 | 07 | X | FRE | @0 Aérospatiale @5 22 |
|---|
| C03 | 07 | X | ENG | @0 Aerospace @5 22 |
|---|
| C03 | 07 | X | SPA | @0 Aeroespacial @5 22 |
|---|
| C03 | 08 | X | FRE | @0 Arithmétique @5 23 |
|---|
| C03 | 08 | X | ENG | @0 Arithmetics @5 23 |
|---|
| C03 | 08 | X | SPA | @0 Aritmética @5 23 |
|---|
| C03 | 09 | X | FRE | @0 Analyse non convexe @5 24 |
|---|
| C03 | 09 | X | ENG | @0 Non convex analysis @5 24 |
|---|
| C03 | 09 | X | SPA | @0 Análisis no convexo @5 24 |
|---|
| N21 | | | | @1 339 |
|---|
| N44 | 01 | | | @1 OTO |
|---|
| N82 | | | | @1 OTO |
|---|
|
|---|
| pR |
| A30 | 01 | 1 | ENG | @1 ICTAC : international colloquium on theoretical aspects of computing @2 2 @3 Hanoi VNM @4 2005-10-17 |
|---|
|
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Le document en format XML
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</keywords><front><div type="abstract" xml:lang="en">We study how to efficiently combine satisfiability procedures built by using a superposition calculus with satisfiability procedures for theories, for which the superposition calculus may not apply (e.g., for various decidable fragments of Arithmetic). Our starting point is the Nelson-Oppen combination method, where satisfiability procedures cooperate by exchanging entailed (disjunction of) equalities between variables. We show that the superposition calculus deduces sufficiently many such equalities for convex theories (e.g., the theory of equality and the theory of lists) and disjunction of equalities for non-convex theories (e.g., the theory of arrays) to guarantee the completeness of the combination method. Experimental results on proof obligations extracted from the certification of auto-generated aerospace software confirm the efficiency of the approach. Finally, we show how to make satisfiability procedures built by superposition both incremental and resettable by using a hierarchic variant of the Nelson-Oppen method.</div>
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</fC01><fC02 i1="01" i2="X"><s0>001D02A05</s0>
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<s5>06</s5>
</fC03><fC03 i1="01" i2="X" l="ENG"><s0>Decidability</s0>
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<s5>07</s5>
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<s5>19</s5>
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<s5>19</s5>
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<s5>20</s5>
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<s5>20</s5>
</fC03><fC03 i1="05" i2="X" l="SPA"><s0>Disyunción</s0>
<s5>20</s5>
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<s5>21</s5>
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<s5>22</s5>
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<s5>22</s5>
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<s5>22</s5>
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<s5>23</s5>
</fC03><fC03 i1="08" i2="X" l="ENG"><s0>Arithmetics</s0>
<s5>23</s5>
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<s5>23</s5>
</fC03><fC03 i1="09" i2="X" l="FRE"><s0>Analyse non convexe</s0>
<s5>24</s5>
</fC03><fC03 i1="09" i2="X" l="ENG"><s0>Non convex analysis</s0>
<s5>24</s5>
</fC03><fC03 i1="09" i2="X" l="SPA"><s0>Análisis no convexo</s0>
<s5>24</s5>
</fC03><fN21><s1>339</s1>
</fN21><fN44 i1="01"><s1>OTO</s1>
</fN44><fN82><s1>OTO</s1>
</fN82><pR><fA30 i1="01" i2="1" l="ENG"><s1>ICTAC : international colloquium on theoretical aspects of computing</s1>
<s2>2</s2>
<s3>Hanoi VNM</s3>
<s4>2005-10-17</s4>
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