Some events seem more random than others. For example, when tossing a coin, a sequence of eight heads in a row does not seem very random. Where do these intuitions about randomness come from? We argue that subjective randomness can be understood as the result of a statistical inference assessing the evidence that an event provides for having been produced by a random generating process. We show...

We introduce and study resource bounded random sets based on Lutz's concept of resource bounded measure ((7, 8]). We concentrate on n c-randomness (c 2) which corresponds to the polynomial time bounded (p-) measure of Lutz, and which is adequate for studying the internal and quantitative structure of E = DTIME(2 lin). However we will also comment on E2 = DTIME(2 pol) and its corresponding (p2-)...

We propose an order index, phi, which gives a quantitative measure of randomness and order of complete genomic sequences. It maps genomes to a number from 0 (random and of infinite length) to 1 (fully ordered) and applies regardless of sequence length. The 786 complete genomic sequences in GenBank were found to have phi values in a very narrow range, phig=0.031(-0.015)+0.028. We show this impli...

If two quantum players at a nonlocal game G achieve a superclassical score, then their measurement outcomes must be at least partially random from the perspective of any third player. This is the basis for device-independent quantum cryptography. In this paper we address a related question: does a superclassical score at G guarantee that one player has created randomness from the perspective of...

Planning with incomplete information may mean a number of di erent things that certain facts of the initial state are not known that operators can have random or nondeterministic e ects or that the plans created contain sensing operations and are branching Study of the com plexity of incomplete information planning has so far been concentrated on probabilistic domains where a number of results ...

We show that paradoxical consequences of violations of Bell’s inequality are induced by the use of an unsuitable probabilistic description for the EPR-Bohm-Bell experiment. The conventional description (due to Bell) is based on a combination of statistical data collected for different settings of polarization beam splitters (PBSs). In fact, such data consists of some conditional probabilities w...

In the theory of algorithmic randomness, several notions of random sequence are defined via a game-theoretic approach, and the notions that received most attention are perhaps Martin-Löf randomness and computable randomness. The latter notion was introduced by Schnorr and is rather natural: an infinite binary sequence is computably random if no total computable strategy succeeds on it by bettin...

Spatial frequency spectra from cervical intraepithelial neoplasia (CIN) tissues are used to detect differences among different grades of human cervical tissues. The randomness of the structures of tissues from normal to different stages of CIN tissues is recognized by analyzing the spatial frequency. This study offers a simpler and better way to recognize the alterations among normal and differ...