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A Linear PCP is a PCP in which the proof is a vector of elements of a finite field , and such that the PCP oracle is only allowed to do linear operations on the proof. Namely, the response from the oracle to a verifier query q ∈ F n {\displaystyle q\in \mathbb {F} ^{n}} is a linear function f ( q , π ) {\displaystyle f(q,\pi )} .
A very useful interactive proof system is PCP(f(n), g(n)), which is a restriction of MA where Arthur can only use f(n) random bits and can only examine g(n) bits of the proof certificate sent by Merlin (essentially using random access). There are a number of easy-to-prove results about various PCP classes.
The PCP theorem states that NP = PCP[O(log n), O(1)],. where PCP[r(n), q(n)] is the class of problems for which a probabilistically checkable proof of a solution can be given, such that the proof can be checked in polynomial time using r(n) bits of randomness and by reading q(n) bits of the proof, correct proofs are always accepted, and incorrect proofs are rejected with probability at least 1/2.
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Verizon settlement payments have started hitting customers' bank accounts as part of a $100 million resolution of a class-action lawsuit. Eligible customers had until April 15 to claim their share ...
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Reindeer, Rangifer tarandus, are familiar hoofed animals that live in cold climates near the North Pole. In many societies, children learn about reindeer from a very early age. This is true even ...
The check digit is calculated by (()), where s is the sum from step 3. This is the smallest number (possibly zero) that must be added to s {\displaystyle s} to make a multiple of 10. Other valid formulas giving the same value are 9 − ( ( s + 9 ) mod 1 0 ) {\displaystyle 9-((s+9){\bmod {1}}0)} , ( 10 − s ) mod 1 0 {\displaystyle (10-s){\bmod ...