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Lecture 5: Universal One-Way Function and Computational Number
... notes on the course website. The lecture notes cover just enough number theory for a student to understand the material in this course. Theorem 2 (Agrawal, Kayal, Saxena) There exists a deterministic polynomial-time algorithm that checks whether a number is prime. See the paper “Primes is in P” for ...
... notes on the course website. The lecture notes cover just enough number theory for a student to understand the material in this course. Theorem 2 (Agrawal, Kayal, Saxena) There exists a deterministic polynomial-time algorithm that checks whether a number is prime. See the paper “Primes is in P” for ...
6= BPP on the hardness of PAC learning On basing ZK
... of circuits) fails to learn the concept class of functions computable by circuits of size n2 under the uniform input distribution1 on all but finitely many input lengths, given access to an example oracle and a membership oracle (see Section 2 for formal definitions). This notion is extremely strong ...
... of circuits) fails to learn the concept class of functions computable by circuits of size n2 under the uniform input distribution1 on all but finitely many input lengths, given access to an example oracle and a membership oracle (see Section 2 for formal definitions). This notion is extremely strong ...
Andras Prekopa (Budapest) (Presented by A. Renyi)
... Applying Theorem 1.2 it follows that the sequence of random variables in (1.19) tends stochastically to 0 as n m ! 1. Thus the Cauchy's convergence criterion holds, hence there is a random variable to which the rst member on the left-hand side of (1.19) converges stochastically. As it can be seen ...
... Applying Theorem 1.2 it follows that the sequence of random variables in (1.19) tends stochastically to 0 as n m ! 1. Thus the Cauchy's convergence criterion holds, hence there is a random variable to which the rst member on the left-hand side of (1.19) converges stochastically. As it can be seen ...
Law of large numbers
In probability theory, the law of large numbers (LLN) is a theorem that describes the result of performing the same experiment a large number of times. According to the law, the average of the results obtained from a large number of trials should be close to the expected value, and will tend to become closer as more trials are performed.The LLN is important because it ""guarantees"" stable long-term results for the averages of some random events. For example, while a casino may lose money in a single spin of the roulette wheel, its earnings will tend towards a predictable percentage over a large number of spins. Any winning streak by a player will eventually be overcome by the parameters of the game. It is important to remember that the LLN only applies (as the name indicates) when a large number of observations are considered. There is no principle that a small number of observations will coincide with the expected value or that a streak of one value will immediately be ""balanced"" by the others (see the gambler's fallacy)