On Boolean vs. modular arithmetic for circuits and communication protocols
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001112 ( PascalFrancis/Corpus );
précédent :
001111;
suivant :
001113
On Boolean vs. modular arithmetic for circuits and communication protocols
Auteurs : C. DammSource :
-
Lecture notes in computer science [ 0302-9743 ] ; 1998.
RBID : Pascal:98-0424917
Descripteurs français
English descriptors
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].
Notice en format standard (ISO 2709)
Pour connaître la documentation sur le format Inist Standard.
| pA |
| A01 | 01 | 1 | | @0 0302-9743 |
|---|
| A05 | | | | @2 1450 |
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| A08 | 01 | 1 | ENG | @1 On Boolean vs. modular arithmetic for circuits and communication protocols |
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| A09 | 01 | 1 | ENG | @1 MFCS'98 : mathematical foundations of computer science 1998 : Brno, 24-28 August 1998 |
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| A11 | 01 | 1 | | @1 DAMM (C.) |
|---|
| A12 | 01 | 1 | | @1 BRIM (Lubos) @9 ed. |
|---|
| A12 | 02 | 1 | | @1 GRUSKA (Josef) @9 ed. |
|---|
| A12 | 03 | 1 | | @1 ZLATUSKA (Jirí) @9 ed. |
|---|
| A14 | 01 | | | @1 University of Trier, Department of Computer Science @2 54296 Trier @3 DEU @Z 1 aut. |
|---|
| A20 | | | | @1 780-788 |
|---|
| A21 | | | | @1 1998 |
|---|
| A23 | 01 | | | @0 ENG |
|---|
| A26 | 01 | | | @0 3-540-64827-5 |
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| A43 | 01 | | | @1 INIST @2 16343 @5 354000070098310760 |
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| A44 | | | | @0 0000 @1 © 1998 INIST-CNRS. All rights reserved. |
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| A45 | | | | @0 8 ref. |
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| A47 | 01 | 1 | | @0 98-0424917 |
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| A60 | | | | @1 P @2 C |
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| A61 | | | | @0 A |
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| A64 | | 1 | | @0 Lecture notes in computer science |
|---|
| A66 | 01 | | | @0 DEU |
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| A66 | 02 | | | @0 USA |
|---|
| C01 | 01 | | ENG | @0 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]. |
|---|
| C02 | 01 | X | | @0 001D02A05 |
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| C03 | 01 | X | FRE | @0 Informatique théorique @5 01 |
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| C03 | 01 | X | ENG | @0 Computer theory @5 01 |
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| C03 | 01 | X | SPA | @0 Informática teórica @5 01 |
|---|
| C03 | 02 | X | FRE | @0 Complexité calcul @5 02 |
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| C03 | 02 | X | ENG | @0 Computational complexity @5 02 |
|---|
| C03 | 02 | X | SPA | @0 Complejidad computación @5 02 |
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| C03 | 03 | X | FRE | @0 Classe complexité @5 03 |
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| C03 | 03 | X | ENG | @0 Complexity class @5 03 |
|---|
| C03 | 03 | X | SPA | @0 Clase complejidad @5 03 |
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| C03 | 04 | 3 | FRE | @0 Algorithme randomisé @5 04 |
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| C03 | 04 | 3 | ENG | @0 Randomised algorithms @5 04 |
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| C03 | 05 | X | FRE | @0 Fonction booléenne @5 05 |
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| C03 | 05 | X | ENG | @0 Boolean function @5 05 |
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| C03 | 05 | X | SPA | @0 Función booliana @5 05 |
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| N21 | | | | @1 285 |
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|
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| pR |
| A30 | 01 | 1 | ENG | @1 Mathematical foundations of computer science. International symposium @2 23 @3 Brno CZE @4 1998-08-24 |
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|
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Format Inist (serveur)
| NO : | PASCAL 98-0424917 INIST |
|---|
| ET : | On Boolean vs. modular arithmetic for circuits and communication protocols |
|---|
| AU : | DAMM (C.); BRIM (Lubos); GRUSKA (Josef); ZLATUSKA (Jirí) |
|---|
| AF : | University of Trier, Department of Computer Science/54296 Trier/Allemagne (1 aut.) |
|---|
| DT : | Publication en série; Congrès; Niveau analytique |
|---|
| SO : | Lecture notes in computer science; ISSN 0302-9743; Allemagne; Da. 1998; Vol. 1450; Pp. 780-788; Bibl. 8 ref. |
|---|
| LA : | Anglais |
|---|
| EA : | 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]. |
|---|
| CC : | 001D02A05 |
|---|
| FD : | Informatique théorique; Complexité calcul; Classe complexité; Algorithme randomisé; Fonction booléenne |
|---|
| ED : | Computer theory; Computational complexity; Complexity class; Randomised algorithms; Boolean function |
|---|
| SD : | Informática teórica; Complejidad computación; Clase complejidad; Función booliana |
|---|
| LO : | INIST-16343.354000070098310760 |
|---|
| ID : | 98-0424917 |
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Links to Exploration step
Pascal:98-0424917
Le document en format XML
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<AU>DAMM (C.); BRIM (Lubos); GRUSKA (Josef); ZLATUSKA (Jirí)</AU>
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