Monomial size vs. Bit-complexity in Sums-of-Squares and Polynomial Calculus
In this paper we consider the relationship between monomial-size and bit-complexity in Sums-of-Squares (SOS) in Polynomial Calculus Resolution over rationals ({\text{PCR}}/\mathbb{Q}). We show that there is a set of polynomial constraints Q n over Boolean variables that has both SOS and {\text{PCR}}...
Uložené v:
| Vydané v: | Proceedings of the 36th Annual ACM/IEEE Symposium on Logic in Computer Science s. 1 - 7 |
|---|---|
| Hlavný autor: | |
| Médium: | Konferenčný príspevok.. |
| Jazyk: | English |
| Vydavateľské údaje: |
IEEE
29.06.2021
|
| Predmet: | |
| On-line prístup: | Získať plný text |
| Tagy: |
Pridať tag
Žiadne tagy, Buďte prvý, kto otaguje tento záznam!
|
| Abstract | In this paper we consider the relationship between monomial-size and bit-complexity in Sums-of-Squares (SOS) in Polynomial Calculus Resolution over rationals ({\text{PCR}}/\mathbb{Q}). We show that there is a set of polynomial constraints Q n over Boolean variables that has both SOS and {\text{PCR}}/\mathbb{Q} refutations of degree 2 and thus with only polynomially many monomials, but for which any SOS or {\text{PCR}}/\mathbb{Q} refutation must have exponential bit-complexity, when the rational coefficients are represented with their reduced fractions written in binary. |
|---|---|
| AbstractList | In this paper we consider the relationship between monomial-size and bit-complexity in Sums-of-Squares (SOS) in Polynomial Calculus Resolution over rationals ({\text{PCR}}/\mathbb{Q}). We show that there is a set of polynomial constraints Q n over Boolean variables that has both SOS and {\text{PCR}}/\mathbb{Q} refutations of degree 2 and thus with only polynomially many monomials, but for which any SOS or {\text{PCR}}/\mathbb{Q} refutation must have exponential bit-complexity, when the rational coefficients are represented with their reduced fractions written in binary. |
| Author | Hakoniemi, Tuomas |
| Author_xml | – sequence: 1 givenname: Tuomas surname: Hakoniemi fullname: Hakoniemi, Tuomas organization: Universitat Politècnica de Catalunya |
| BookMark | eNotj9tKxDAURSMoqGO_QJD8QGtOmqTJoxYvgxWF6vOQ5gKRtB2bVqxfr-A8bViwFuxzdDyMg0PoCkgBQNR1s61bTqlgBSUUCsUqwhk_QpmqJAjBGZOKi1OUpfRBCKGyAsLUGXp6HoexDzriFH4c_koFvg1zbsZ-H913mFccBtwufcpHn7efi55cwnqw-HWM68GsdTRLXNIFOvE6JpcddoPe7-_e6se8eXnY1jdNrqlUcw7UQOest5x3YKwCxb0vO6pNZa1UVSlAU9YxDlZ5Irgg4I3jUhJP_wgtN-jyvxucc7v9FHo9rbvD5fIXTs1PTA |
| ContentType | Conference Proceeding |
| DBID | 6IE 6IH CBEJK RIE RIO |
| DOI | 10.1109/LICS52264.2021.9470545 |
| DatabaseName | IEEE Electronic Library (IEL) Conference Proceedings IEEE Proceedings Order Plan (POP) 1998-present by volume IEEE Xplore All Conference Proceedings IEEE Xplore IEEE Proceedings Order Plans (POP) 1998-present |
| DatabaseTitleList | |
| Database_xml | – sequence: 1 dbid: RIE name: IEEE Electronic Library (IEL) url: https://ieeexplore.ieee.org/ sourceTypes: Publisher |
| DeliveryMethod | fulltext_linktorsrc |
| Discipline | Computer Science |
| EISBN | 9781665448956 1665448954 |
| EndPage | 7 |
| ExternalDocumentID | 9470545 |
| Genre | orig-research |
| GroupedDBID | 6IE 6IH ACM ALMA_UNASSIGNED_HOLDINGS APO CBEJK GUFHI LHSKQ RIE RIO |
| ID | FETCH-LOGICAL-a289t-12c1bedfd55b1cd9195ff3b2ac7dd897361a24b451d9f065601fce5880f2d9f23 |
| IEDL.DBID | RIE |
| ISICitedReferencesCount | 2 |
| ISICitedReferencesURI | http://www.webofscience.com/api/gateway?GWVersion=2&SrcApp=Summon&SrcAuth=ProQuest&DestLinkType=CitingArticles&DestApp=WOS_CPL&KeyUT=000947350400019&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D |
| IngestDate | Wed Aug 27 02:26:37 EDT 2025 |
| IsPeerReviewed | false |
| IsScholarly | true |
| Language | English |
| LinkModel | DirectLink |
| MergedId | FETCHMERGED-LOGICAL-a289t-12c1bedfd55b1cd9195ff3b2ac7dd897361a24b451d9f065601fce5880f2d9f23 |
| PageCount | 7 |
| ParticipantIDs | ieee_primary_9470545 |
| PublicationCentury | 2000 |
| PublicationDate | 2021-June-29 |
| PublicationDateYYYYMMDD | 2021-06-29 |
| PublicationDate_xml | – month: 06 year: 2021 text: 2021-June-29 day: 29 |
| PublicationDecade | 2020 |
| PublicationTitle | Proceedings of the 36th Annual ACM/IEEE Symposium on Logic in Computer Science |
| PublicationTitleAbbrev | LICS |
| PublicationYear | 2021 |
| Publisher | IEEE |
| Publisher_xml | – name: IEEE |
| SSID | ssj0002871049 |
| Score | 2.2046702 |
| Snippet | In this paper we consider the relationship between monomial-size and bit-complexity in Sums-of-Squares (SOS) in Polynomial Calculus Resolution over rationals... |
| SourceID | ieee |
| SourceType | Publisher |
| StartPage | 1 |
| SubjectTerms | Calculus Computer science |
| Title | Monomial size vs. Bit-complexity in Sums-of-Squares and Polynomial Calculus |
| URI | https://ieeexplore.ieee.org/document/9470545 |
| WOSCitedRecordID | wos000947350400019&url=https%3A%2F%2Fcvtisr.summon.serialssolutions.com%2F%23%21%2Fsearch%3Fho%3Df%26include.ft.matches%3Dt%26l%3Dnull%26q%3D |
| hasFullText | 1 |
| inHoldings | 1 |
| isFullTextHit | |
| isPrint | |
| link | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwlV1NSwMxEA1t8eCpait-k4NH0252s5vmarEo1lKoSm8ln7BQd7W7W9Rfb5KuFcGLtxAYAhOGvJnMmwfAZaIGgmLuRiGyBBGuJRIWNSBjTBBIxjT20gnPYzqZDOZzNm2Aqy0XRmvtm890zy39X77KZeVKZX1GqEUYcRM0KU02XK1tPcUhf4t2axIwDlh_fDecOXThKich7tXGv1RU_CMyav_v-D3Q_WHjwen2ndkHDZ0dgPa3HAOso7MD7h88x5gvYZF-arguevA6LZFvGtfvFm3DNIOz6qVAuUGzt8oxjyDPFJzmy4_acsiXrh5YdMHT6OZxeItqrQTEbcpUIhxKLLQyKo4FlophFhsTiZBLqtSA0SjBPCSCxFgxE7iJO9hIHdvoNaHdCaND0MryTB8ByK2tTEhgBIlIEggWRJwYm4FLL2mjjkHH-WbxuhmHsajdcvL39inYde533VUhOwOtclXpc7Aj12VarC78HX4BBf-dZQ |
| linkProvider | IEEE |
| linkToHtml | http://cvtisr.summon.serialssolutions.com/2.0.0/link/0/eLvHCXMwlV3PS8MwFA5zCnqauom_zcGj2Zo2bZerw-FYNwabstvITyjMVtd2qH-9SVcnghdvIfAgvEd4X17e9z4AbgPZ5SFmdhQiDRBhSiBuUAPSWjuOoFThUjrhOQrH4-58Tic1cLflwiilyuYz1bbL8i9fpqKwpbIOJaFBGP4O2PUJcZ0NW2tbUbHY3-DdigaMHdqJBr2pxRe2duLidmX-S0elTCP9xv8OcAhaP3w8ONlmmiNQU8kxaHwLMsDqfjbBcFSyjNkSZvGnguusDe_jHJVt4-rd4G0YJ3BavGQo1Wj6VljuEWSJhJN0-VFZ9tjSVgSzFnjqP8x6j6hSS0DMPJpyhF2BuZJa-j7HQlJMfa097jIRStmloRdg5hJOfCypduzMHayF8s391a7Zcb0TUE_SRJ0CyIytCIijOfFI4HDqeIxo8wYXpaiNPANN65vF62YgxqJyy_nf2zdg_3E2ihbRYDy8AAc2FLbXyqWXoJ6vCnUF9sQ6j7PVdRnPL2VloKw |
| 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%3Abook&rft.genre=proceeding&rft.title=Proceedings+of+the+36th+Annual+ACM%2FIEEE+Symposium+on+Logic+in+Computer+Science&rft.atitle=Monomial+size+vs.+Bit-complexity+in+Sums-of-Squares+and+Polynomial+Calculus&rft.au=Hakoniemi%2C+Tuomas&rft.date=2021-06-29&rft.pub=IEEE&rft.spage=1&rft.epage=7&rft_id=info:doi/10.1109%2FLICS52264.2021.9470545&rft.externalDocID=9470545 |