Mathematical proofs | Randomized algorithms
In computational complexity theory, a probabilistically checkable proof (PCP) is a type of proof that can be checked by a randomized algorithm using a bounded amount of randomness and reading a bounded number of bits of the proof. The algorithm is then required to accept correct proofs and reject incorrect proofs with very high probability. A standard proof (or certificate), as used in the verifier-based definition of the complexity class NP, also satisfies these requirements, since the checking procedure deterministically reads the whole proof, always accepts correct proofs and rejects incorrect proofs. However, what makes them interesting is the existence of probabilistically checkable proofs that can be checked by reading only a few bits of the proof using randomness in an essential way. Probabilistically checkable proofs give rise to many complexity classes depending on the number of queries required and the amount of randomness used. The class PCP[r(n),q(n)] refers to the set of decision problems that have probabilistically checkable proofs that can be verified in polynomial time using at most r(n) random bits and by reading at most q(n) bits of the proof. Unless specified otherwise, correct proofs should always be accepted, and incorrect proofs should be rejected with probability greater than 1/2. The PCP theorem, a major result in computational complexity theory, states that PCP[O(log n),O(1)] = NP. (Wikipedia).
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This video provides an introduction to the proof method of proof by counter example. mathispower4u.com
From playlist Symbolic Logic and Proofs (Discrete Math)
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More resources available at www.misterwootube.com
From playlist The Nature of Proof
On Low-Degree Polynomials - Madhu Sudan
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From playlist Mathematics
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From playlist Symbolic Logic and Proofs (Discrete Math)
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This video provides 3 examples of statements and which proof method should be used. mathispower4u.com
From playlist Symbolic Logic and Proofs (Discrete Math)
Panorama of Mathematics: Michel Goemans
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Stanford Seminar: Building Systems Using Malicious Components
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From playlist Stanford EE380-Colloquium on Computer Systems - Seminar Series
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Bayesian Inference by Program Verification - Joost-Pieter Katoen, RWTH Aachen University
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From playlist Logic and learning workshop
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Henry Yuen: Testing low-degree polynomials in the noncommutative setting
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From playlist Global Noncommutative Geometry Seminar (Americas)
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The Abel Prize announcement 2021 - Avi Wigderson and László Lovász
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Abel Prize award ceremony 2021
The ceremony honours both the 2020-winners, Hillel Furstenberg and Gregory Margulis, and the 2021-winners, Avi Wigderson and László́ Lovász. 0:30 Haddy N'jie sings Feeling Good 3:18 Welcome by Master of ceremonies, Haddy N'jie 4:46 On the nomination process and the work of the Abel Prize
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Constant Rate PCPs for Circuit-SAT with Sublinear Query Complexity - Eli Ben-Sasson
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