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Probabilistically Checkable Arguments [chapter]

Yael Tauman Kalai, Ran Raz
2009 Lecture Notes in Computer Science  
A 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).  ... 
doi:10.1007/978-3-642-03356-8_9 fatcat:ddxecjularezjcuejagrt655wm

On the Work of Madhu Sudan: the 2002 Nevalinna Prize Winner [article]

Shafi Goldwasser
2002 arXiv   pre-print
This short note will be devoted to describing Sudan's work on 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?  ... 
arXiv:cs/0212056v1 fatcat:5hhycpl7czh2vcefcl7vy4kb4i

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.  ... 

Probabilistic Proof Systems [chapter]

Oded Goldreich
1999 Modern Cryptography, Probabilistic Proofs and Pseudorandomness  
In this exposition, we concentrate on three such proof systems -interactive proofs, zero-knowledge proofs, and 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  ... 
doi:10.1007/978-3-662-12521-2_2 fatcat:344npt7j6rb6vdyw5alybqm4dq

Probabilistic Proof Systems [chapter]

Oded Goldreich
1995 Proceedings of the International Congress of Mathematicians  
In this exposition, we concentrate on three such proof systems -interactive proofs, zero-knowledge proofs, and 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  ... 
doi:10.1007/978-3-0348-9078-6_134 fatcat:3asgnxrbhrbmpcbk2eqlqisua4

Probabilistic proof systems — A survey [chapter]

Oded Goldreich
1997 Lecture Notes in Computer Science  
In this exposition, we concentrate on three such proof systems -interactive proofs, zero-knowledge proofs, and 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.  ... 
doi:10.1007/bfb0023492 fatcat:dmjknckobrghtkdnqu67gd4pw4

Probabilistic Proof Systems

Oded Goldreich
1994 BRICS Report Series  
In this exposition, we concentrate on three such proof systems -- interactive proofs, zero-knowledge proofs, and 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.  ... 
doi:10.7146/brics.v1i28.21643 fatcat:g7noy5g7p5fu5kvgcsodz2v3ty

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.  ... 

Plaintext-Checkable Encryption [chapter]

Sébastien Canard, Georg Fuchsbauer, Aline Gouget, Fabien Laguillaumie
2012 Lecture Notes in Computer Science  
Deterministic/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  ... 
doi:10.1007/978-3-642-27954-6_21 fatcat:ur4pmqah2fb57hmg2cfzs2vly4

Succinct NP Proofs from an Extractability Assumption [chapter]

Giovanni Di Crescenzo, Helger Lipmaa
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) 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  ... 
doi:10.1007/978-3-540-69407-6_21 fatcat:4wvsrt32sbcmjcigkuxbgeuw7q

Polylogarithmic two-round argument systems

Thilo Mie
2008 Journal of Mathematical Cryptology  
We construct a concrete database-aware PIR scheme and build our 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  ... 
doi:10.1515/jmc.2008.016 fatcat:65a52ljxrzamrbtfv7w2222hva

The tale of the PCP theorem

Dana Moshkovitz
2012 XRDS Crossroads The ACM Magazine for Students  
increase by more than a sub-linear factor to make the format probabilistically checkable.  ...  The theorem became known as the PCP Theorem, where PCP stands for "Probabilistically Checkable Proofs".  ... 
doi:10.1145/2090276.2090286 fatcat:aim67yzrxrhsnjfs72dkfomzae

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  ... 

Debates with small transparent quantum verifiers [article]

Abuzer Yakaryilmaz and A. C. Cem Say, H. Gökalp Demirci
2015 arXiv   pre-print
As mentioned in Section 2, languages with debates 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  ... 
arXiv:1405.1655v2 fatcat:i6t2e4n3wvemxigqm43y6usrai

Checking generalized debates with small space and randomness [article]

H. Gökalp Demirci, A. C. Cem Say
2012 arXiv   pre-print
Our model combines and generalizes the concepts of one-way interactive proof systems, games of incomplete information, and 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.  ... 
arXiv:1211.7346v1 fatcat:jlkzwpkb3nfl7nwakdsq7z3gz4
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