Related papers: The Probability Spaces of QuickSort
These are lecture notes written at the University of Zurich during spring 2014 and spring 2015. The first part of the notes gives an introduction to probability theory. It explains the notion of random events and random variables,…
Perhaps surprisingly, it is possible to predict how long an algorithm will take to run on a previously unseen input, using machine learning techniques to build a model of the algorithm's runtime as a function of problem-specific instance…
This work presents a comparison for the performance of sequential sorting algorithms under four different modes of execution, the sequential processing mode, a conventional multi-threading implementation, multi-threading with OpenMP Library…
Hardware, systems and algorithms research communities have historically had different incentive structures and fluctuating motivation to engage with each other explicitly. This historical treatment is odd given that hardware and software…
When algorithms for sorting and searching are applied to keys that are represented as bit strings, we can quantify the performance of the algorithms not only in terms of the number of key comparisons required by the algorithms but also in…
We present the first algorithm for computing class groups and unit groups of arbitrary number fields that provably runs in probabilistic subexponential time, assuming the Extended Riemann Hypothesis (ERH). Previous subexponential algorithms…
The probability distribution P from which the history of our universe is sampled represents a theory of everything or TOE. We assume P is formally describable. Since most (uncountably many) distributions are not, this imposes a strong…
A succesful method to describe the asymptotic behavior of a discrete time stochastic process governed by some recursive formula is to relate it to the limit sets of a well chosen mean differential equation. Under an attainability condition,…
The aim of this paper is to present an elementary computable theory of probability, random variables and stochastic processes. The probability theory is baed on existing approaches using valuations and lower integrals. Various approaches to…
We study the origin of the Born probability rule rho = |psi|^2 in the de Broglie-Bohm pilot-wave formulation of quantum theory. It is argued that quantum probabilities arise dynamically, and have a status similar to thermal probabilities in…
We define the class of "simple recursive games". A simple recursive game is defined as a simple stochastic game (a notion due to Anne Condon), except that we allow arbitrary real payoffs but disallow moves of chance. We study the complexity…
This paper extends the quantum search class of algorithms to the multiple solution case. It is shown that, like the basic search algorithm, these too can be represented as a rotation in an appropriately defined two dimensional vector space.…
The symmetry of quantum theory under time reversal has long been a subject of controversy because the transition probabilities given by Born's rule do not apply backward in time. Here, we resolve this problem within a rigorous operational…
This paper generalizes the notion of stochastic order to a relation between probability measures over arbitrary measurable spaces. This generalization is motivated by the observation that for the stochastic ordering of two stationary Markov…
We present a method for computing probability of occurence of 1s in a configuration obtained by iteration of a probabilistic cellular automata (PCA), starting from a random initial configuration. If the PCA is sufficiently simple, one can…
We consider reversible random walks in random environment obtained from symmetric long--range jump rates on a random point process. We prove almost sure transience and recurrence results under suitable assumptions on the point process and…
The observed probabilities of quantum mechanics possess a time asymmetry which is based on the truism that a state must be prepared before an observable can be measured in it. While Hilbert space quantum theory cannot incorporate this arrow…
The execution time of programs is a key element in many areas of computer science, mainly those where achieving good performance (e.g., scheduling in cloud computing) or a predictable one (e.g., meeting deadlines in embedded systems) is the…
In this work we consider the problem of searches that utilises past information gathered during searching, to evaluate the probability distribution of finding the source at each step. We start with a sample strategy where the movement at…
Though the ability of human beings to deal with probabilities has been put into question, the assessment of rarity is a crucial competence underlying much of human decision-making and is pervasive in spontaneous narrative behaviour. This…