On Boolean vs. Modular arithmetic for circuits and communication protocols
Identifieur interne : 002289 ( Main/Exploration ); précédent : 002288; suivant : 002290On Boolean vs. Modular arithmetic for circuits and communication protocols
Auteurs : Carsten Damm [Allemagne]Source :
- Lecture Notes in Computer Science [ 0302-9743 ] ; 1998.
Descripteurs français
- Pascal (Inist)
English descriptors
- KwdEn :
Abstract
Abstract: We compare two computational models that appeared in the literature in a Boolean setting and in an analog setting based on modular arithmetic. We prove that in both cases the arithmetic version can to some extend simulate the Boolean version. Although the models are very different, the proofs rely on the same idea based on the Schwartz-Zippel-Theorem. In the first part we prove that depth d semi-unbounded Boolean circuits can be simulated by depth 2d + O(log d + log n) semi-unbounded arithmetic circuits, regardless of the size. This is an improvement on a similar construction in [3] that achieves depth 3d + O(log s + log n), where s is the size of the original circuit. Our construction is simpler and uses fewer random bits. In the second part we prove, that two-party parity communication protocols can approximate nondeterministic communication protocols. A strict simulation of one by the other is impossible as was shown in [2].
Url:
DOI: 10.1007/BFb0055829
Affiliations:
Links toward previous steps (curation, corpus...)
- to stream Istex, to step Corpus: 001296
- to stream Istex, to step Curation: 001184
- to stream Istex, to step Checkpoint: 000E60
- to stream Main, to step Merge: 002678
- to stream PascalFrancis, to step Corpus: 001112
- to stream PascalFrancis, to step Curation: 001713
- to stream PascalFrancis, to step Checkpoint: 000E83
- to stream Main, to step Merge: 002754
- to stream Main, to step Curation: 002289
Le document en format XML
<record><TEI wicri:istexFullTextTei="biblStruct"><teiHeader><fileDesc><titleStmt><title xml:lang="en">On Boolean vs. Modular arithmetic for circuits and communication protocols</title><author><name sortKey="Damm, Carsten" sort="Damm, Carsten" uniqKey="Damm C" first="Carsten" last="Damm">Carsten Damm</name></author></titleStmt><publicationStmt><idno type="wicri:source">ISTEX</idno><idno type="RBID">ISTEX:8B735DF5093FB7A183856D1B9A7B094101A52447</idno><date when="1998" year="1998">1998</date><idno type="doi">10.1007/BFb0055829</idno><idno type="url">https://api.istex.fr/document/8B735DF5093FB7A183856D1B9A7B094101A52447/fulltext/pdf</idno><idno type="wicri:Area/Istex/Corpus">001296</idno><idno type="wicri:explorRef" wicri:stream="Istex" wicri:step="Corpus" wicri:corpus="ISTEX">001296</idno><idno type="wicri:Area/Istex/Curation">001184</idno><idno type="wicri:Area/Istex/Checkpoint">000E60</idno><idno type="wicri:explorRef" wicri:stream="Istex" wicri:step="Checkpoint">000E60</idno><idno type="wicri:doubleKey">0302-9743:1998:Damm C:on:boolean:vs</idno><idno type="wicri:Area/Main/Merge">002678</idno><idno type="wicri:source">INIST</idno><idno type="RBID">Pascal:98-0424917</idno><idno type="wicri:Area/PascalFrancis/Corpus">001112</idno><idno type="wicri:Area/PascalFrancis/Curation">001713</idno><idno type="wicri:Area/PascalFrancis/Checkpoint">000E83</idno><idno type="wicri:explorRef" wicri:stream="PascalFrancis" wicri:step="Checkpoint">000E83</idno><idno type="wicri:doubleKey">0302-9743:1998:Damm C:on:boolean:vs</idno><idno type="wicri:Area/Main/Merge">002754</idno><idno type="wicri:Area/Main/Curation">002289</idno><idno type="wicri:Area/Main/Exploration">002289</idno></publicationStmt><sourceDesc><biblStruct><analytic><title level="a" type="main" xml:lang="en">On Boolean vs. Modular arithmetic for circuits and communication protocols</title><author><name sortKey="Damm, Carsten" sort="Damm, Carsten" uniqKey="Damm C" first="Carsten" last="Damm">Carsten Damm</name><affiliation wicri:level="4"><country xml:lang="fr">Allemagne</country><wicri:regionArea>Department of Computer Science, University of Trier, D-54296, Trier</wicri:regionArea><orgName type="university">Université de Trèves</orgName><placeName><settlement type="city">Trèves (Allemagne)</settlement><region type="land" nuts="1">Rhénanie-Palatinat</region></placeName></affiliation><affiliation wicri:level="1"><country wicri:rule="url">Allemagne</country></affiliation></author></analytic><monogr></monogr><series><title level="s">Lecture Notes in Computer Science</title><imprint><date>1998</date></imprint><idno type="ISSN">0302-9743</idno><idno type="eISSN">1611-3349</idno><idno type="ISSN">0302-9743</idno></series><idno type="istex">8B735DF5093FB7A183856D1B9A7B094101A52447</idno><idno type="DOI">10.1007/BFb0055829</idno><idno type="ChapterID">76</idno><idno type="ChapterID">Chap76</idno></biblStruct></sourceDesc><seriesStmt><idno type="ISSN">0302-9743</idno></seriesStmt></fileDesc><profileDesc><textClass><keywords scheme="KwdEn" xml:lang="en"><term>Boolean function</term><term>Complexity class</term><term>Computational complexity</term><term>Computer theory</term><term>Randomised algorithms</term></keywords><keywords scheme="Pascal" xml:lang="fr"><term>Algorithme randomisé</term><term>Classe complexité</term><term>Complexité calcul</term><term>Fonction booléenne</term><term>Informatique théorique</term></keywords></textClass><langUsage><language ident="en">en</language></langUsage></profileDesc></teiHeader><front><div type="abstract" xml:lang="en">Abstract: We compare two computational models that appeared in the literature in a Boolean setting and in an analog setting based on modular arithmetic. We prove that in both cases the arithmetic version can to some extend simulate the Boolean version. Although the models are very different, the proofs rely on the same idea based on the Schwartz-Zippel-Theorem. In the first part we prove that depth d semi-unbounded Boolean circuits can be simulated by depth 2d + O(log d + log n) semi-unbounded arithmetic circuits, regardless of the size. This is an improvement on a similar construction in [3] that achieves depth 3d + O(log s + log n), where s is the size of the original circuit. Our construction is simpler and uses fewer random bits. In the second part we prove, that two-party parity communication protocols can approximate nondeterministic communication protocols. A strict simulation of one by the other is impossible as was shown in [2].</div></front></TEI><affiliations><list><country><li>Allemagne</li></country><region><li>Rhénanie-Palatinat</li></region><settlement><li>Trèves (Allemagne)</li></settlement><orgName><li>Université de Trèves</li></orgName></list><tree><country name="Allemagne"><region name="Rhénanie-Palatinat"><name sortKey="Damm, Carsten" sort="Damm, Carsten" uniqKey="Damm C" first="Carsten" last="Damm">Carsten Damm</name></region><name sortKey="Damm, Carsten" sort="Damm, Carsten" uniqKey="Damm C" first="Carsten" last="Damm">Carsten Damm</name></country></tree></affiliations></record>Pour manipuler ce document sous Unix (Dilib)
EXPLOR_STEP=$WICRI_ROOT/Wicri/Rhénanie/explor/UnivTrevesV1/Data/Main/Exploration
HfdSelect -h $EXPLOR_STEP/biblio.hfd -nk 002289 | SxmlIndent | more
Ou
HfdSelect -h $EXPLOR_AREA/Data/Main/Exploration/biblio.hfd -nk 002289 | SxmlIndent | more
Pour mettre un lien sur cette page dans le réseau Wicri
{{Explor lien
|wiki= Wicri/Rhénanie
|area= UnivTrevesV1
|flux= Main
|étape= Exploration
|type= RBID
|clé= ISTEX:8B735DF5093FB7A183856D1B9A7B094101A52447
|texte= On Boolean vs. Modular arithmetic for circuits and communication protocols
}}
| This area was generated with Dilib version V0.6.31. |  |