Some Bridging Results and Challenges in Classical, Quantum and Computational Randomness

Giuseppe Longo 1 Catuscia Palamidessi 2 Paul Thierry 1
2 COMETE - Concurrency, Mobility and Transactions
LIX - Laboratoire d'informatique de l'École polytechnique [Palaiseau], Inria Saclay - Ile de France
Abstract : We encountered randomness in our dierent elds of interest, as unpredictable phenomena are omnipresent in natural and articial processes. In classical physical systems (and by this we mean also relativistic ones) randomness may be dened as 'deterministic unpredictability'. That is, since Poincare's results (on the Three Body Problem) and his invention of the geometry of dynamical systems, deterministic systems include various forms of chaotic ones, from weak (mixing) systems to ones highly sensitive to border conditions, where random behaviours are part of the deterministic evolutions. Randomness got a new status with the birth of quantum mechanics: access to information on a given systems passes through a nondeterministic process (measurement). In computer sciences, randomness is at the core of algorithmic information theory, all the while nondeterministic algorithms and networks present crucial random aspects. Finally, an extensive use of randomness is made also in biology. Thus we wondered: all these dierent sciences refer to a concept of randomness, but is it really the same concept? And if they are dierent concepts, what is the relation between them?
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Giuseppe Longo, Catuscia Palamidessi, Paul Thierry. Some Bridging Results and Challenges in Classical, Quantum and Computational Randomness. Hector Zenil. Randomness Through Computation, World Scientific, pp.NA, 2011. ⟨hal-00445553v3⟩

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