On Boolean vs. modular arithmetic for circuits and communication protocols
Identifieur interne : 000E83 ( PascalFrancis/Checkpoint ); précédent : 000E82; suivant : 000E84On Boolean vs. modular arithmetic for circuits and communication protocols
Auteurs : C. Damm [Allemagne]Source :
- Lecture notes in computer science [ 0302-9743 ] ; 1998.
Descripteurs français
- Pascal (Inist)
English descriptors
- KwdEn :
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].
Affiliations:
Links toward previous steps (curation, corpus...)
Links to Exploration step
Pascal:98-0424917Le document en format XML
<record><TEI><teiHeader><fileDesc><titleStmt><title xml:lang="en" level="a">On Boolean vs. modular arithmetic for circuits and communication protocols</title><author><name sortKey="Damm, C" sort="Damm, C" uniqKey="Damm C" first="C." last="Damm">C. Damm</name><affiliation wicri:level="4"><inist:fA14 i1="01"><s1>University of Trier, Department of Computer Science</s1><s2>54296 Trier</s2><s3>DEU</s3><sZ>1 aut.</sZ></inist:fA14><country>Allemagne</country><wicri:noRegion>54296 Trier</wicri:noRegion><wicri:noRegion>Department of Computer Science</wicri:noRegion><wicri:noRegion>54296 Trier</wicri:noRegion><orgName type="university">Université de Trèves</orgName><placeName><settlement type="city">Trèves (Allemagne)</settlement><region type="land" nuts="1">Rhénanie-Palatinat</region></placeName></affiliation></author></titleStmt><publicationStmt><idno type="wicri:source">INIST</idno><idno type="inist">98-0424917</idno><date when="1998">1998</date><idno type="stanalyst">PASCAL 98-0424917 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></publicationStmt><sourceDesc><biblStruct><analytic><title xml:lang="en" level="a">On Boolean vs. modular arithmetic for circuits and communication protocols</title><author><name sortKey="Damm, C" sort="Damm, C" uniqKey="Damm C" first="C." last="Damm">C. Damm</name><affiliation wicri:level="4"><inist:fA14 i1="01"><s1>University of Trier, Department of Computer Science</s1><s2>54296 Trier</s2><s3>DEU</s3><sZ>1 aut.</sZ></inist:fA14><country>Allemagne</country><wicri:noRegion>54296 Trier</wicri:noRegion><wicri:noRegion>Department of Computer Science</wicri:noRegion><wicri:noRegion>54296 Trier</wicri:noRegion><orgName type="university">Université de Trèves</orgName><placeName><settlement type="city">Trèves (Allemagne)</settlement><region type="land" nuts="1">Rhénanie-Palatinat</region></placeName></affiliation></author></analytic><series><title level="j" type="main">Lecture notes in computer science</title><idno type="ISSN">0302-9743</idno><imprint><date when="1998">1998</date></imprint></series></biblStruct></sourceDesc><seriesStmt><title level="j" type="main">Lecture notes in computer science</title><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>Informatique théorique</term><term>Complexité calcul</term><term>Classe complexité</term><term>Algorithme randomisé</term><term>Fonction booléenne</term></keywords></textClass></profileDesc></teiHeader><front><div type="abstract" xml:lang="en">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><inist><standard h6="B"><pA><fA01 i1="01" i2="1"><s0>0302-9743</s0></fA01><fA05><s2>1450</s2></fA05><fA08 i1="01" i2="1" l="ENG"><s1>On Boolean vs. modular arithmetic for circuits and communication protocols</s1></fA08><fA09 i1="01" i2="1" l="ENG"><s1>MFCS'98 : mathematical foundations of computer science 1998 : Brno, 24-28 August 1998</s1></fA09><fA11 i1="01" i2="1"><s1>DAMM (C.)</s1></fA11><fA12 i1="01" i2="1"><s1>BRIM (Lubos)</s1><s9>ed.</s9></fA12><fA12 i1="02" i2="1"><s1>GRUSKA (Josef)</s1><s9>ed.</s9></fA12><fA12 i1="03" i2="1"><s1>ZLATUSKA (Jirí)</s1><s9>ed.</s9></fA12><fA14 i1="01"><s1>University of Trier, Department of Computer Science</s1><s2>54296 Trier</s2><s3>DEU</s3><sZ>1 aut.</sZ></fA14><fA20><s1>780-788</s1></fA20><fA21><s1>1998</s1></fA21><fA23 i1="01"><s0>ENG</s0></fA23><fA26 i1="01"><s0>3-540-64827-5</s0></fA26><fA43 i1="01"><s1>INIST</s1><s2>16343</s2><s5>354000070098310760</s5></fA43><fA44><s0>0000</s0><s1>© 1998 INIST-CNRS. All rights reserved.</s1></fA44><fA45><s0>8 ref.</s0></fA45><fA47 i1="01" i2="1"><s0>98-0424917</s0></fA47><fA60><s1>P</s1><s2>C</s2></fA60><fA61><s0>A</s0></fA61><fA64 i2="1"><s0>Lecture notes in computer science</s0></fA64><fA66 i1="01"><s0>DEU</s0></fA66><fA66 i1="02"><s0>USA</s0></fA66><fC01 i1="01" l="ENG"><s0>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].</s0></fC01><fC02 i1="01" i2="X"><s0>001D02A05</s0></fC02><fC03 i1="01" i2="X" l="FRE"><s0>Informatique théorique</s0><s5>01</s5></fC03><fC03 i1="01" i2="X" l="ENG"><s0>Computer theory</s0><s5>01</s5></fC03><fC03 i1="01" i2="X" l="SPA"><s0>Informática teórica</s0><s5>01</s5></fC03><fC03 i1="02" i2="X" l="FRE"><s0>Complexité calcul</s0><s5>02</s5></fC03><fC03 i1="02" i2="X" l="ENG"><s0>Computational complexity</s0><s5>02</s5></fC03><fC03 i1="02" i2="X" l="SPA"><s0>Complejidad computación</s0><s5>02</s5></fC03><fC03 i1="03" i2="X" l="FRE"><s0>Classe complexité</s0><s5>03</s5></fC03><fC03 i1="03" i2="X" l="ENG"><s0>Complexity class</s0><s5>03</s5></fC03><fC03 i1="03" i2="X" l="SPA"><s0>Clase complejidad</s0><s5>03</s5></fC03><fC03 i1="04" i2="3" l="FRE"><s0>Algorithme randomisé</s0><s5>04</s5></fC03><fC03 i1="04" i2="3" l="ENG"><s0>Randomised algorithms</s0><s5>04</s5></fC03><fC03 i1="05" i2="X" l="FRE"><s0>Fonction booléenne</s0><s5>05</s5></fC03><fC03 i1="05" i2="X" l="ENG"><s0>Boolean function</s0><s5>05</s5></fC03><fC03 i1="05" i2="X" l="SPA"><s0>Función booliana</s0><s5>05</s5></fC03><fN21><s1>285</s1></fN21></pA><pR><fA30 i1="01" i2="1" l="ENG"><s1>Mathematical foundations of computer science. International symposium</s1><s2>23</s2><s3>Brno CZE</s3><s4>1998-08-24</s4></fA30></pR></standard></inist><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, C" sort="Damm, C" uniqKey="Damm C" first="C." last="Damm">C. Damm</name></region></country></tree></affiliations></record>Pour manipuler ce document sous Unix (Dilib)
EXPLOR_STEP=$WICRI_ROOT/Wicri/Rhénanie/explor/UnivTrevesV1/Data/PascalFrancis/Checkpoint
HfdSelect -h $EXPLOR_STEP/biblio.hfd -nk 000E83 | SxmlIndent | more
Ou
HfdSelect -h $EXPLOR_AREA/Data/PascalFrancis/Checkpoint/biblio.hfd -nk 000E83 | SxmlIndent | more
Pour mettre un lien sur cette page dans le réseau Wicri
{{Explor lien
|wiki= Wicri/Rhénanie
|area= UnivTrevesV1
|flux= PascalFrancis
|étape= Checkpoint
|type= RBID
|clé= Pascal:98-0424917
|texte= On Boolean vs. modular arithmetic for circuits and communication protocols
}}
| This area was generated with Dilib version V0.6.31. |  |