Modularity and Combination of Associative Commutative Congruence Closure Algorithms enriched with Semantic Properties
Algorithms for computing congruence closure of ground equations over uninterpreted symbols and interpreted symbols satisfying associativity and commutativity (AC) properties are proposed. The algorithms are based on a framework for computing a congruence closure by abstracting nonflat terms by const...
Gespeichert in:
| Veröffentlicht in: | Logical methods in computer science Jg. 19, Issue 1 |
|---|---|
| 1. Verfasser: | |
| Format: | Journal Article |
| Sprache: | Englisch |
| Veröffentlicht: |
Logical Methods in Computer Science e.V
14.03.2023
|
| Schlagworte: | |
| ISSN: | 1860-5974, 1860-5974 |
| Online-Zugang: | Volltext |
| Tags: |
Tag hinzufügen
Keine Tags, Fügen Sie den ersten Tag hinzu!
|
| Abstract | Algorithms for computing congruence closure of ground equations over
uninterpreted symbols and interpreted symbols satisfying associativity and
commutativity (AC) properties are proposed. The algorithms are based on a
framework for computing a congruence closure by abstracting nonflat terms by
constants as proposed first in Kapur's congruence closure algorithm (RTA97).
The framework is general, flexible, and has been extended also to develop
congruence closure algorithms for the cases when associative-commutative
function symbols can have additional properties including idempotency,
nilpotency, identities, cancellativity and group properties as well as their
various combinations. Algorithms are modular; their correctness and termination
proofs are simple, exploiting modularity. Unlike earlier algorithms, the
proposed algorithms neither rely on complex AC compatible well-founded
orderings on nonvariable terms nor need to use the associative-commutative
unification and extension rules in completion for generating canonical rewrite
systems for congruence closures. They are particularly suited for integrating
into the Satisfiability modulo Theories (SMT) solvers. A new way to view
Groebner basis algorithm for polynomial ideals with integer coefficients as a
combination of the congruence closures over the AC symbol * with the identity 1
and the congruence closure over an Abelian group with + is outlined. |
|---|---|
| AbstractList | Algorithms for computing congruence closure of ground equations over
uninterpreted symbols and interpreted symbols satisfying associativity and
commutativity (AC) properties are proposed. The algorithms are based on a
framework for computing a congruence closure by abstracting nonflat terms by
constants as proposed first in Kapur's congruence closure algorithm (RTA97).
The framework is general, flexible, and has been extended also to develop
congruence closure algorithms for the cases when associative-commutative
function symbols can have additional properties including idempotency,
nilpotency, identities, cancellativity and group properties as well as their
various combinations. Algorithms are modular; their correctness and termination
proofs are simple, exploiting modularity. Unlike earlier algorithms, the
proposed algorithms neither rely on complex AC compatible well-founded
orderings on nonvariable terms nor need to use the associative-commutative
unification and extension rules in completion for generating canonical rewrite
systems for congruence closures. They are particularly suited for integrating
into the Satisfiability modulo Theories (SMT) solvers. A new way to view
Groebner basis algorithm for polynomial ideals with integer coefficients as a
combination of the congruence closures over the AC symbol * with the identity 1
and the congruence closure over an Abelian group with + is outlined. Algorithms for computing congruence closure of ground equations over uninterpreted symbols and interpreted symbols satisfying associativity and commutativity (AC) properties are proposed. The algorithms are based on a framework for computing a congruence closure by abstracting nonflat terms by constants as proposed first in Kapur's congruence closure algorithm (RTA97). The framework is general, flexible, and has been extended also to develop congruence closure algorithms for the cases when associative-commutative function symbols can have additional properties including idempotency, nilpotency, identities, cancellativity and group properties as well as their various combinations. Algorithms are modular; their correctness and termination proofs are simple, exploiting modularity. Unlike earlier algorithms, the proposed algorithms neither rely on complex AC compatible well-founded orderings on nonvariable terms nor need to use the associative-commutative unification and extension rules in completion for generating canonical rewrite systems for congruence closures. They are particularly suited for integrating into the Satisfiability modulo Theories (SMT) solvers. A new way to view Groebner basis algorithm for polynomial ideals with integer coefficients as a combination of the congruence closures over the AC symbol * with the identity 1 and the congruence closure over an Abelian group with + is outlined. |
| Author | Kapur, Deepak |
| Author_xml | – sequence: 1 givenname: Deepak surname: Kapur fullname: Kapur, Deepak |
| BookMark | eNpNkUlLBDEQhYOM4PoHPOWoh9Ys3Vm8DYPLwIiCeg7pdPUY6U4k6Vb89_aMC9ah6r0q-Ch4B2gWYgCETig5LwXT6qLrXS6oPqWXVJ8xwvgO2qdKkKLSspz903voOOdXMhXnVDGxj8a72IydTX74xDY0eBH72gc7-BhwbPE85-j8ZN9hc-rH4VeHdRohuEl2MY8J8Lxbxwnz0mcMIXn3Ag3-mDx-hN6GwTv8kOIbpMFDPkK7re0yHP_MQ_R8ffW0uC1W9zfLxXxVOFpxXkhSa0GIslAp5RxxVDoHtVCW0baVZdswUtZC1FK2LQFZO6kbVjairqkCq_khWn5zm2hfzVvyvU2fJlpvtouY1sZOD7kODGOgGskEMM1LLpmWljArSVVppxlnE4t9s1yKOSdo_3iUmG0OZpODodrQTdvkwL8AnJaALA |
| ContentType | Journal Article |
| DBID | AAYXX CITATION DOA |
| DOI | 10.46298/lmcs-19(1:19)2023 |
| DatabaseName | CrossRef Directory of Open Access Journals (DOAJ) |
| DatabaseTitle | CrossRef |
| DatabaseTitleList | CrossRef |
| Database_xml | – sequence: 1 dbid: DOA name: DOAJ Directory of Open Access Journals url: https://www.doaj.org/ sourceTypes: Open Website |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Computer Science |
| EISSN | 1860-5974 |
| ExternalDocumentID | oai_doaj_org_article_22e8d726e293437297a02a70559c9232 10_46298_lmcs_19_1_19_2023 |
| GroupedDBID | .4S .DC 29L 2WC 5GY 5VS AAFWJ AAYXX ADBBV ADMLS ADQAK AENEX AFPKN ALMA_UNASSIGNED_HOLDINGS ARCSS BCNDV CITATION EBS EJD FRP GROUPED_DOAJ J9A KQ8 MK~ ML~ M~E OK1 OVT P2P TR2 TUS XSB |
| ID | FETCH-LOGICAL-c1533-70b96008ae588cc0c17cceb68a21ff74fd204b66b77ff0e7bc79d24d6bb18ea93 |
| IEDL.DBID | DOA |
| ISSN | 1860-5974 |
| IngestDate | Fri Oct 03 12:51:30 EDT 2025 Sat Nov 29 06:21:52 EST 2025 |
| IsDoiOpenAccess | true |
| IsOpenAccess | true |
| IsPeerReviewed | true |
| IsScholarly | true |
| Language | English |
| License | https://creativecommons.org/licenses/by/4.0 |
| LinkModel | DirectLink |
| MergedId | FETCHMERGED-LOGICAL-c1533-70b96008ae588cc0c17cceb68a21ff74fd204b66b77ff0e7bc79d24d6bb18ea93 |
| OpenAccessLink | https://doaj.org/article/22e8d726e293437297a02a70559c9232 |
| ParticipantIDs | doaj_primary_oai_doaj_org_article_22e8d726e293437297a02a70559c9232 crossref_primary_10_46298_lmcs_19_1_19_2023 |
| PublicationCentury | 2000 |
| PublicationDate | 2023-03-14 |
| PublicationDateYYYYMMDD | 2023-03-14 |
| PublicationDate_xml | – month: 03 year: 2023 text: 2023-03-14 day: 14 |
| PublicationDecade | 2020 |
| PublicationTitle | Logical methods in computer science |
| PublicationYear | 2023 |
| Publisher | Logical Methods in Computer Science e.V |
| Publisher_xml | – name: Logical Methods in Computer Science e.V |
| SSID | ssj0000331826 |
| Score | 2.2625406 |
| Snippet | Algorithms for computing congruence closure of ground equations over
uninterpreted symbols and interpreted symbols satisfying associativity and
commutativity... Algorithms for computing congruence closure of ground equations over uninterpreted symbols and interpreted symbols satisfying associativity and commutativity... |
| SourceID | doaj crossref |
| SourceType | Open Website Index Database |
| SubjectTerms | computer science - logic in computer science |
| Title | Modularity and Combination of Associative Commutative Congruence Closure Algorithms enriched with Semantic Properties |
| URI | https://doaj.org/article/22e8d726e293437297a02a70559c9232 |
| Volume | 19, Issue 1 |
| hasFullText | 1 |
| inHoldings | 1 |
| isFullTextHit | |
| isPrint | |
| journalDatabaseRights | – providerCode: PRVAON databaseName: DOAJ Directory of Open Access Journals customDbUrl: eissn: 1860-5974 dateEnd: 99991231 omitProxy: false ssIdentifier: ssj0000331826 issn: 1860-5974 databaseCode: DOA dateStart: 20040101 isFulltext: true titleUrlDefault: https://www.doaj.org/ providerName: Directory of Open Access Journals – providerCode: PRVHPJ databaseName: ROAD: Directory of Open Access Scholarly Resources customDbUrl: eissn: 1860-5974 dateEnd: 99991231 omitProxy: false ssIdentifier: ssj0000331826 issn: 1860-5974 databaseCode: M~E dateStart: 20040101 isFulltext: true titleUrlDefault: https://road.issn.org providerName: ISSN International Centre |
| link | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwrV1LSwMxEA4iHrz4Ft_k4EGRxU2a5uGtlhYPKoIPvC3ZPKrQdqWtPfrbncm2Uk9evIRlCUP4Jpv5ZnYyQ8gphgFzD96JFE0HDorXWSlEzCI3YGydMTbd4n-5Vff3-vXVPCy0-sKcsLo8cA3cJedBe8VlALuU_jEpm3OLNWCMA3KSTl9gPQvOVDqDGw0kzvUtGSG50Zf9gRtnzJyxK2bOsWn4L0u0ULA_WZbuBlmbUULaqpeySZbCcIusz9st0NnXt00-7yqPSaPAmyn4_xRmgFubkKVVpD9ATwNN1z4m8-dhb5TSpWm7X2FAkLb6vQrEvA3GFLYPJoN6igFZ-hgGgPS7ow8Yox9hsdUd8tztPLVvslnXhMwhd8tUXoJXkmsbmlo7lzumnAul1JYzUIyInueilLJUKsY8qNIp47nwsiyZDtY0dsnysBqGPUJBUIwSGExgRsgmN8xaJrxquhiAOtl9cjFHsPioi2MU4FQkvAvEu2CmYDgg3vvkGkH-mYmFrdMLUHcxU3fxl7oP_kPIIVnFBWEqGRNHZHkCWjgmK246eR-PTtJOgvHuq_MNR4nOYA |
| linkProvider | Directory of Open Access Journals |
| openUrl | ctx_ver=Z39.88-2004&ctx_enc=info%3Aofi%2Fenc%3AUTF-8&rfr_id=info%3Asid%2Fsummon.serialssolutions.com&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Ajournal&rft.genre=article&rft.atitle=Modularity+and+Combination+of+Associative+Commutative+Congruence+Closure+Algorithms+enriched+with+Semantic+Properties&rft.jtitle=Logical+methods+in+computer+science&rft.au=Kapur%2C+Deepak&rft.date=2023-03-14&rft.issn=1860-5974&rft.eissn=1860-5974&rft.volume=19%2C+Issue+1&rft_id=info:doi/10.46298%2Flmcs-19%281%3A19%292023&rft.externalDBID=n%2Fa&rft.externalDocID=10_46298_lmcs_19_1_19_2023 |
| thumbnail_l | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/lc.gif&issn=1860-5974&client=summon |
| thumbnail_m | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/mc.gif&issn=1860-5974&client=summon |
| thumbnail_s | http://covers-cdn.summon.serialssolutions.com/index.aspx?isbn=/sc.gif&issn=1860-5974&client=summon |