Random Generation of Trees: Random Generators in Computer Science

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In , Austrian mathematician Richard von Mises proposed that a binary sequence is random if the proportion of zeros and ones approaches 50 per cent and if this property is also true for any sub-sequence generated by simple rules.

Generating random binary trees — A survey - ScienceDirect

Taking the alternating sequence , it is clear that zeros and ones occur with equal frequency, but the sub-sequence formed by taking every second number contains only ones, which is clearly not random. The Russian mathematician Andrey Kolmogorov defined the complexity of a binary sequence in terms of the length of the shortest computer program or algorithm that can generate it. A non-random sequence has patterns that enable it to be expressed in a form more compact than its complete list of bits.

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Thus, non-random sequences are compressible. Randomness and incompressibility are equivalent concepts. No computational algorithm can generate a truly random binary sequence. This is simple to explain: any sequence produced by a computer program is automatically compressed to the length of the program.

If it is truly random, the program must be of length comparable to the sequence, and we might just as well list it directly. So, any number that is computable is non-random. The best we can do is to generate long sequences that have some of the key properties of random numbers.

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The programs that do this are called pseudo-random number generators. Pseudo-random number generators are algorithms that use mathematical formulae to produce sequences of numbers. These sequences are deterministic: they are predicted by the algorithm. However, they appear completely random and satisfy various statistical conditions for randomness.

1.2. Better pseudorandom number generators

The algorithms vary in quality: the best are very good, the worst are very bad. True random number generators extract randomness from physical phenomena that are completely unpredictable. Atmospheric noise produces numbers that pass all statistical checks for randomness. For 20 years, Dr Mads Haahr of the school of computer science and statistics at Trinity College, Dublin has been using atmospheric noise to produce random numbers for the website random.

The data is used for lotteries and sweepstakes, to drive online games, for scientific applications and for art and music. The system now uses a distributed configuration with receivers in different geographic locations, and the results are subjected to a battery of statistical tests to give confidence in the randomness of the numbers. He blogs a t thatsmaths. There is a hypothesis that eating ultraprocessed foods can disrupt signals between the gut and the brain, encouraging us to keep eating.

The extensive Princeton Companion to Mathematics overview even needed a companion volume.

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  5. Random numbers plucked from the atmosphere Randomness defies precise definition despite attempts to define it over the years Tue, Dec 4, , Peter Lynch. What is randomness?

    Why are countries creating public random number generators?

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    Want to help combat climate change? Start by planting a tree. Electric vehicles are gathering pace. Commenting on The Irish Times has changed. To comment you must now be an Irish Times subscriber. And the importance of true randomness is not to be underestimated, he adds. There are devices that generate numbers that claim to be truly random. They rely on unpredictable processes like thermal or atmospheric noise rather than human-defined patterns.

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