Proving the PCP-Theorem

1998 ◽  
pp. 83-160 ◽  
Author(s):  
Volker Heun ◽  
Wolfgang Merkle ◽  
Ulrich Weigand
Keyword(s):  
Pcp Theorem

scholarly journals An algebraic proof of the real number PCP theorem

2017 ◽  
Vol 40 ◽  
pp. 34-77 ◽  
Author(s):  
Martijn Baartse ◽  
Klaus Meer
Keyword(s):  
Real Number ◽  
Algebraic Proof ◽  
The Real ◽  
Pcp Theorem

scholarly journals On Dinur's proof of the PCP theorem

2006 ◽  
Vol 44 (01) ◽  
pp. 19-62 ◽  
Author(s):  
Jaikumar Radhakrishnan ◽  
Madhu Sudan
Keyword(s):  
Pcp Theorem

scholarly journals Quantum Information and the PCP Theorem

Algorithmica ◽  
2007 ◽  
Vol 55 (3) ◽  
pp. 462-489 ◽  
Author(s):  
Ran Raz
Keyword(s):  
Quantum Information ◽  
Pcp Theorem

A Combinatorial Consistency Lemma with Application to Proving the PCP Theorem

2000 ◽  
Vol 29 (4) ◽  
pp. 1132-1154 ◽  
Author(s):  
Oded Goldreich ◽  
Shmuel Safra
Keyword(s):  
Pcp Theorem

scholarly journals Assignment Testers: Towards a Combinatorial Proof of the PCP Theorem

2006 ◽  
Vol 36 (4) ◽  
pp. 975-1024 ◽  
Author(s):  
Irit Dinur ◽  
Omer Reingold
Keyword(s):  
Combinatorial Proof ◽  
Pcp Theorem

scholarly journals MIP* = RE

2021 ◽  
Vol 64 (11) ◽  
pp. 131-138
Author(s):  
Zhengfeng Ji ◽  
Anand Natarajan ◽  
Thomas Vidick ◽  
John Wright ◽  
Henry Yuen
Keyword(s):  
Operator Algebras ◽  
Foundations Of Quantum Mechanics ◽  
Research Community ◽  
Hardness Of Approximation ◽  
Surprising Result ◽  
Open Problems ◽  
Recursively Enumerable ◽  
Pcp Theorem ◽  
Efficient Verification ◽  
Probabilistic Polynomial Time

Note from the Research Highlights Co-Chairs: A Research Highlights paper appearing in Communications is usually peer-reviewed prior to publication. The following paper is unusual in that it is still under review. However, the result has generated enormous excitement in the research community, and came strongly nominated by SIGACT, a nomination seconded by external reviewers. The complexity class NP characterizes the collection of computational problems that have efficiently verifiable solutions. With the goal of classifying computational problems that seem to lie beyond NP, starting in the 1980s complexity theorists have considered extensions of the notion of efficient verification that allow for the use of randomness (the class MA), interaction (the class IP), and the possibility to interact with multiple proofs, or provers (the class MIP). The study of these extensions led to the celebrated PCP theorem and its applications to hardness of approximation and the design of cryptographic protocols. In this work, we study a fourth modification to the notion of efficient verification that originates in the study of quantum entanglement. We prove the surprising result that every problem that is recursively enumerable, including the Halting problem, can be efficiently verified by a classical probabilistic polynomial-time verifier interacting with two all-powerful but noncommunicating provers sharing entanglement. The result resolves long-standing open problems in the foundations of quantum mechanics (Tsirelson's problem) and operator algebras (Connes' embedding problem).

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