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Landauer's principle states that the minimum energy needed to erase one bit of information is proportional to the temperature at which the system is operating. Specifically, the energy needed for this computational task is given by. where is the Boltzmann constant and is the temperature in Kelvin. [ 2] At room temperature, the Landauer limit ...
Adding 4 hours to 9 o'clock gives 1 o'clock, since 13 is congruent to 1 modulo 12. In mathematics, modular arithmetic is a system of arithmetic for integers, where numbers "wrap around" when reaching a certain value, called the modulus. The modern approach to modular arithmetic was developed by Carl Friedrich Gauss in his book Disquisitiones ...
Exponent of a power of two. Graph of log2 xas a function of a positive real number x. In mathematics, the binary logarithm(log2 n) is the powerto which the number 2must be raisedto obtain the value n. That is, for any real number x, x=log2n 2x=n.{\displaystyle x=\log _{2}n\quad \Longleftrightarrow \quad 2^{x}=n.}
Two's complement is the most common method of representing signed (positive, negative, and zero) integers on computers, [1] and more generally, fixed point binary values. Two's complement uses the binary digit with the greatest value as the sign to indicate whether the binary number is positive or negative; when the most significant bit is 1 the number is signed as negative and when the most ...
Péter Gács showed that BPP is actually contained in Σ 2 ∩ Π 2. Clemens Lautemann contributed by giving a simple proof of BPP’s membership in Σ 2 ∩ Π 2, also in 1983. It is conjectured that in fact BPP=P, which is a much stronger statement than the Sipser–Lautemann theorem.
Implicit in the definition is the condition that the algorithm, , must decide based on a single sample from one of the distributions. One might conceive of a situation in which the algorithm trying to distinguish between two distributions, could access as many samples as it needed. Hence two ensembles that cannot be distinguished by polynomial ...
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For this case we prove a weaker version of the theorem: One-way permutation → pseudorandom generator. A one-way permutation is a one-way function that is also a permutation of the input bits. A pseudorandom generator can be constructed from one-way permutation ƒ as follows: Gl : {0,1} l → {0,1} l+1 = ƒ ( x ).