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Probabilistically Checkable Arguments
[chapter]

2009
*
Lecture Notes in Computer Science
*

A

doi:10.1007/978-3-642-03356-8_9
fatcat:ddxecjularezjcuejagrt655wm
*probabilistically**checkable**argument*(PCA) is a relaxation of the notion of*probabilistically**checkable*proof (PCP). ... We give a general reduction that converts any public-coin interactive proof into a one-round (two-message)*argument*. ... In this paper, we consider the relaxed setting of*probabilistically**checkable**argument*(PCA). ...##
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On the Work of Madhu Sudan: the 2002 Nevalinna Prize Winner
[article]

2002
*
arXiv
*
pre-print

This short note will be devoted to describing Sudan's work on

arXiv:cs/0212056v1
fatcat:5hhycpl7czh2vcefcl7vy4kb4i
*probabilistically**checkable*proofs -- the so called PCP theorem and its implications. ... The first work shows a*probabilistic*characterization of the class NP -- those sets for which short and easily*checkable*proofs of membership exist, and demonstrates consequences of this characterization ... Are*probabilistically**checkable*proofs more powerful than the deterministic NP style proofs? ...##
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Page 8121 of Mathematical Reviews Vol. , Issue 2000k
[page]

2000
*
Mathematical Reviews
*

Dantsin intro- duces a new model of

*probabilistically**checkable*proof systems, called*probabilistically**checkable*proof calculi. ... a PSPACE-hard problem that is*probabilistically**checkable*by the model introduced. ...##
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Probabilistic Proof Systems
[chapter]

1999
*
Modern Cryptography, Probabilistic Proofs and Pseudorandomness
*

In this exposition, we concentrate on three such proof systems -interactive proofs, zero-knowledge proofs, and

doi:10.1007/978-3-662-12521-2_2
fatcat:344npt7j6rb6vdyw5alybqm4dq
*probabilistic**checkable*proofs -stressing the essential role of randomness in each of them ... Various types of*probabilistic*proof systems have played a central role in the development of computer science in the last decade. ... DEFINITION 3 (*Probabilistic**Checkable*Proofs -PCP): (1) A*probabilistic**checkable*proof (PCP) system for a set S is a*probabilistic*polynomial-time oracle machine (called verifier), denoted V, satisfying ...##
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Probabilistic Proof Systems
[chapter]

1995
*
Proceedings of the International Congress of Mathematicians
*

In this exposition, we concentrate on three such proof systems -interactive proofs, zero-knowledge proofs, and

doi:10.1007/978-3-0348-9078-6_134
fatcat:3asgnxrbhrbmpcbk2eqlqisua4
*probabilistic**checkable*proofs -stressing the essential role of randomness in each of them ... Various types of*probabilistic*proof systems have played a central role in the development of computer science in the last decade. ... DEFINITION 3 (*Probabilistic**Checkable*Proofs -PCP): (1) A*probabilistic**checkable*proof (PCP) system for a set S is a*probabilistic*polynomial-time oracle machine (called verifier), denoted V, satisfying ...##
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Probabilistic proof systems — A survey
[chapter]

1997
*
Lecture Notes in Computer Science
*

In this exposition, we concentrate on three such proof systems -interactive proofs, zero-knowledge proofs, and

doi:10.1007/bfb0023492
fatcat:dmjknckobrghtkdnqu67gd4pw4
*probabilistic**checkable*proofs -stressing the essential role of randomness in each of them ... Various types of*probabilistic*proof systems have played a central role in the development of computer science in the last decade. ... Definition 5 (*Probabilistic**Checkable*Proofs -PCP): 1. ...##
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Probabilistic Proof Systems

1994
*
BRICS Report Series
*

In this exposition, we concentrate on three such proof systems -- interactive proofs, zero-knowledge proofs, and

doi:10.7146/brics.v1i28.21643
fatcat:g7noy5g7p5fu5kvgcsodz2v3ty
*probabilistic**checkable*proofs -- stressing the essential role of randomness in each of ... Various types of*probabilistic*proof systems have played a central role in the development of computer science in the last decade. ... De nition 5 (*Probabilistic**Checkable*Proofs { PCP): 1. ...##
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Page 2182 of Mathematical Reviews Vol. , Issue 2000c
[page]

2000
*
Mathematical Reviews
*

They build upon a sequence of beautiful previous results on

*probabilistically**checkable*proofs. ... Using this frame- work, it presents self-contained proofs of several previous results on*probabilistically**checkable*proofs, as well as new results. ...##
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Plaintext-Checkable Encryption
[chapter]

2012
*
Lecture Notes in Computer Science
*

Deterministic/

doi:10.1007/978-3-642-27954-6_21
fatcat:ur4pmqah2fb57hmg2cfzs2vly4
*probabilistic*encryption, unlinkability, group signature with VLR and backward unlinkability. ... We define a new cryptographic primitive called plaintext-*checkable*encryption (PCE), which extends public-key encryption by the following functionality: given a plaintext, a ciphertext and a public key ... A plaintext-*checkable*encryption scheme is a*probabilistic*public-key encryption scheme with the additional functionality that anyone can test whether a ciphertext c is the encryption of a given plaintext ...##
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Succinct NP Proofs from an Extractability Assumption
[chapter]

2008
*
Lecture Notes in Computer Science
*

We prove, using a non-standard complexity assumption, that any language in N P has a 1-round (that is, the verifier sends a message to the prover, and the prover sends a message to the verifier)

doi:10.1007/978-3-540-69407-6_21
fatcat:4wvsrt32sbcmjcigkuxbgeuw7q
*argument*...*Probabilistically**Checkable*Proof (PCP) Systems. ... We say that (P, V ) is a (non-adaptive)*probabilistically**checkable*proof system for L if there exists a polynomial q and negligible functions δ c , δ s such that (P, V ) is a (nonadaptive)*probabilistically*...##
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Polylogarithmic two-round argument systems

2008
*
Journal of Mathematical Cryptology
*

We construct a concrete database-aware PIR scheme and build our

doi:10.1515/jmc.2008.016
fatcat:65a52ljxrzamrbtfv7w2222hva
*argument*system by combining a database-aware PIR scheme with a*probabilistically**checkable*proof system (PCP). ... We present a two-round*argument*system for NP languages with polylogarithmic communication complexity. ...*Probabilistically**checkable*proofs (PCPs) In a*probabilistically**checkable*proof (PCP) system the verifier V has oracle access to a proof tape π, such that on query i it reads the i-th bit of the string ...##
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The tale of the PCP theorem

2012
*
XRDS Crossroads The ACM Magazine for Students
*

increase by more than a sub-linear factor to make the format

doi:10.1145/2090276.2090286
fatcat:aim67yzrxrhsnjfs72dkfomzae
*probabilistically**checkable*. ... The theorem became known as the PCP Theorem, where PCP stands for "*Probabilistically**Checkable*Proofs". ...##
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Page 6983 of Mathematical Reviews Vol. , Issue 96k
[page]

1996
*
Mathematical Reviews
*

[Steger, Angelika] (D-HUMB-I; Berlin)

*Probabilistically**checkable*proofs and their consequences for approximation algorithms. (English summary) Trends in discrete mathematics. ... Hastad’s switching lemma [in Proceedings of the Eighteenth Annual ACM Symposium on Theory of Computing (Berkeley, CA, 1986), 6-20, ACM Press, New York, 1986], eliminating the*probabilistic**argument*altogether ...##
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Debates with small transparent quantum verifiers
[article]

2015
*
arXiv
*
pre-print

As mentioned in Section 2, languages with debates

arXiv:1405.1655v2
fatcat:i6t2e4n3wvemxigqm43y6usrai
*checkable*by deterministic finite state verifiers are regular, whereas*probabilistic*verifiers can handle some nonregular languages when some error is ... We can therefore also state that every language in the class EXPTIME has such a "partial-information" debate*checkable*by a private-coin multiple-head two-way*probabilistic*finite automaton with zero error ...##
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Checking generalized debates with small space and randomness
[article]

2012
*
arXiv
*
pre-print

Our model combines and generalizes the concepts of one-way interactive proof systems, games of incomplete information, and

arXiv:1211.7346v1
fatcat:jlkzwpkb3nfl7nwakdsq7z3gz4
*probabilistically**checkable*complete-information debate systems. ... The classes of languages with debates*checkable*by verifiers operating under severe bounds on the memory and randomness are studied. ... For partial-information debates, we modify the*argument*above to take the increased ignorance of P1 about the state of V into account. ...
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