Do Most Strong Deenitions of Randomness Exist? Ecole Normale Supérieure De Lyon Do Most Strong Deenitions of Randomness Exist? Do Most Strong Deenitions of Randomness Exist?
نویسندگان
چکیده
The goal of our paper is to propose a way to obtain more re ned de nitions of randomness than the notions known so far e g Martin L of randomness We show that a perfect de nition of randomness based on provability does not exist We then weaken our require ments on the de nition by replacing provability by consistency and obtain a formula that de nes a set of random sequences that ful lls rather strong conditions
منابع مشابه
Quantum Randomness and Nondeterminism
Does the notion of a quantum randomized or nondeterministic algorithm make sense, and if so, does quantum randomness or nonde-terminism add power? Although reasonable quantum random sources do not add computational power, the discussion of quantum random-ness naturally leads to several deenitions of the complexity of quantum states. Unlike classical string complexity, both deterministic and non...
متن کاملFull randomness from arbitrarily deterministic events.
Do completely unpredictable events exist? Classical physics excludes fundamental randomness. Although quantum theory makes probabilistic predictions, this does not imply that nature is random, as randomness should be certified without relying on the complete structure of the theory being used. Bell tests approach the question from this perspective. However, they require prior perfect randomness...
متن کاملEcole Normale Supérieure de Cachan 61 , avenue du Président Wilson 94235 Cachan Cedex France
Well-structured transition systems (WSTS's) are a general class of innnite state systems for which decidability results rely on the existence of a well-quasi-ordering between states that is compatible with the transitions. In this article, we provide an extensive treatment of the WSTS idea and show several new results. Our improved deenitions allow many examples of classical systems to be seen ...
متن کاملFaster Randomness Testing with the NIST Statistical Test Suite
Randomness testing plays an important role in cryptography. Randomness is typically examined by batteries of statistical tests. One of the most frequently used test batteries is the NIST Statistical Test Suite. The tests of randomness should be rather fast since they usually process large volumes of data. Unfortunately, this is not the case for the NIST STS, where a complete test can take hours...
متن کاملStrong to fragile transition in a model of liquid silica
The transport properties of an ionic model for liquid silica [1] at high temperatures and pressure are investigated using molecular dynamics simulations. With increasing pressure, a clear change from ”strong” to ”fragile” behaviour (according to Angell’s classification of glass-forming liquids) is observed, albeit only on the small viscosity range that can be explored in MD simulations. This ch...
متن کامل