ECCC-Report TR11-104https://eccc.weizmann.ac.il/report/2011/104Comments and Revisions published for TR11-104en-usMon, 07 Jan 2013 15:30:07 +0200
Revision 3
| Combinatorial PCPs with efficient verifiers |
Or Meir
https://eccc.weizmann.ac.il/report/2011/104#revision3The PCP theorem asserts the existence of proofs that can be verified by a verifier that reads only a very small part of the proof. The theorem was originally proved by Arora and Safra (J. ACM 45(1)) and Arora et al. (J. ACM 45(3)) using sophisticated algebraic tools. More than a decade later, Dinur (J. ACM 54(3)) gave a simpler and arguably more intuitive proof using alternative combinatorial techniques.
One disadvantage of Dinur's proof compared to the previous algebraic proof is that it yields less efficient verifiers. In this work, we provide a combinatorial construction of PCPs with verifiers that are as efficient as the ones obtained by the algebraic methods. The result is the first combinatorial proof of the PCP theorem for NEXP (originally proved by Babai et al., FOCS 1990), and a combinatorial construction of super-fast PCPs of Proximity for NP (first constructed by Ben-Sasson et al., CCC 2005).Mon, 07 Jan 2013 15:30:07 +0200https://eccc.weizmann.ac.il/report/2011/104#revision3
Revision 2
| Combinatorial PCPs with efficient verifiers |
Or Meir
https://eccc.weizmann.ac.il/report/2011/104#revision2The PCP theorem asserts the existence of proofs that can be verified by a verifier that reads only a very small part of the proof. The theorem was originally proved by Arora and Safra (J. ACM 45(1)) and Arora et al. (J. ACM 45(3)) using sophisticated algebraic tools. More than a decade later, Dinur (J. ACM 54(3)) gave a simpler and arguably more intuitive proof using alternative combinatorial techniques.
One disadvantage of Dinur's proof compared to the previous algebraic proof is that it yields less efficient verifiers. In this work, we provide a combinatorial construction of PCPs with verifiers that are as efficient as the ones obtained by the algebraic methods. The result is the first combinatorial proof of the PCP theorem for NEXP (originally proved by Babai et al., FOCS 1990), and a combinatorial construction of super-fast PCPs of Proximity for NP (first constructed by Ben-Sasson et al., CCC 2005).Mon, 31 Dec 2012 17:37:08 +0200https://eccc.weizmann.ac.il/report/2011/104#revision2
Revision 1
| Combinatorial PCPs with efficient verifiers |
Or Meir
https://eccc.weizmann.ac.il/report/2011/104#revision1The PCP theorem asserts the existence of proofs that can be verified by a verifier that reads only a very small part of the proof. The theorem was originally proved by Arora and Safra (J. ACM 45(1)) and Arora et al. (J. ACM 45(3)) using sophisticated algebraic tools. More than a decade later, Dinur (J. ACM 54(3)) gave a simpler and arguably more intuitive proof using alternative combinatorial techniques.
One disadvantage of Dinur's proof compared to the previous algebraic proof is that it yields less efficient verifiers. In this work, we provide a combinatorial construction of PCPs with verifiers that are as efficient as the ones obtained by the algebraic methods. The result is the first combinatorial proof of the PCP theorem for NEXP (originally proved by Babai et al., FOCS 1990), and a combinatorial construction of super-fast PCPs of Proximity for NP (first constructed by Ben-Sasson et al., CCC 2005).Wed, 03 Aug 2011 21:57:58 +0300https://eccc.weizmann.ac.il/report/2011/104#revision1
Paper TR11-104
| Combinatorial PCPs with efficient verifiers |
Or Meir
https://eccc.weizmann.ac.il/report/2011/104The PCP theorem asserts the existence of proofs that can be verified by a verifier that reads only a very small part of the proof. The theorem was originally proved by Arora and Safra (J. ACM 45(1)) and Arora et al. (J. ACM 45(3)) using sophisticated algebraic tools. More than a decade later, Dinur (J. ACM 54(3)) gave a simpler and arguably more intuitive proof using alternative combinatorial techniques.
One disadvantage of Dinur's proof compared to the previous algebraic proof is that it yields less efficient verifiers. In this work, we provide a combinatorial construction of PCPs with verifiers that are as efficient as the ones obtained by the algebraic methods. The result is the first combinatorial proof of the PCP theorem for NEXP (originally proved by Babai et al., FOCS 1990), and a combinatorial construction of super-fast PCPs of Proximity for NP (first constructed by Ben-Sasson et al., CCC 2005).Wed, 03 Aug 2011 19:36:29 +0300https://eccc.weizmann.ac.il/report/2011/104