Search results for "PROBABILITY"
showing 10 items of 3417 documents
Quantum Walks with Multiple or Moving Marked Locations
2008
We study some properties of quantum walks on the plane. First, we discuss the behavior of quantum walks when moving marked locations are introduced. Second, we present an exceptional case, when quantum walk fails to find any of the marked locations.
Dimensions of random affine code tree fractals
2014
We calculate the almost sure Hausdorff dimension for a general class of random affine planar code tree fractals. The set of probability measures describing the randomness includes natural measures in random $V$-variable and homogeneous Markov constructions.
On symmetric nonlocal games
2013
Abstract Nonlocal games are used to display differences between the classical and quantum world. In this paper, we study symmetric XOR games, which form an important subset of nonlocal games. We give simple methods for calculating the classical and the quantum values for symmetric XOR games with one-bit input per player. We illustrate those methods with two examples. One example is an N -player game (due to Ardehali (1992) [3] ) that provides the maximum quantum-over-classical advantage. The second example comes from generalization of CHSH game by letting the referee to choose arbitrary symmetric distribution of players’ inputs.
Grover’s Algorithm with Errors
2013
Grover’s algorithm is a quantum search algorithm solving the unstructured search problem of size n in \(O(\sqrt{n})\) queries, while any classical algorithm needs O(n) queries [3].
A formal proof of the ε-optimality of absorbing continuous pursuit algorithms using the theory of regular functions
2014
Published version of an article from the journal: Applied Intelligence. Also available on Springerlink: http://dx.doi.org/10.1007/s10489-014-0541-1 The most difficult part in the design and analysis of Learning Automata (LA) consists of the formal proofs of their convergence accuracies. The mathematical techniques used for the different families (Fixed Structure, Variable Structure, Discretized etc.) are quite distinct. Among the families of LA, Estimator Algorithms (EAs) are certainly the fastest, and within this family, the set of Pursuit algorithms have been considered to be the pioneering schemes. Informally, if the environment is stationary, their ε-optimality is defined as their abili…
Application of kolmogorov complexity to inductive inference with limited memory
1995
A b s t r a c t . We consider inductive inference with limited memory[l]. We show that there exists a set U of total recursive functions such that U can be learned with linear long-term memory (and no short-term memory); U can be learned with logarithmic long-term memory (and some amount of short-term memory); if U is learned with sublinear long-term memory, then the short-term memory exceeds arbitrary recursive function. Thus an open problem posed by Freivalds, Kinber and Smith[l] is solved. To prove our result, we use Kolmogorov complexity.
Regularity of one-letter languages acceptable by 2-way finite probabilistic automata
1991
R. Freivalds proved that the nonregular language {0m1m} can be recognized by 2-way probabilistic finite automata (2pfa) with arbitrarily high probability 1-e (e>0). We prove that such an effect is impossible for one-letter languages: every one-letter language acceptable by 2pfa with an isolated cutpoint is regular.
Centering and Compound Conditionals under Coherence
2016
There is wide support in logic , philosophy , and psychology for the hypothesis that the probability of the indicative conditional of natural language, \(P(\textit{if } A \textit{ then } B)\), is the conditional probability of B given A, P(B|A). We identify a conditional which is such that \(P(\textit{if } A \textit{ then } B)= P(B|A)\) with de Finetti’s conditional event, B|A. An objection to making this identification in the past was that it appeared unclear how to form compounds and iterations of conditional events. In this paper, we illustrate how to overcome this objection with a probabilistic analysis, based on coherence, of these compounds and iterations. We interpret the compounds a…
The Infinite-Valued Łukasiewicz Logic and Probability
2017
The paper concerns the algebraic structure of the set of cumulative distribution functions as well as the relationship between the resulting algebra and the infinite-valued Łukasiewicz algebra. The paper also discusses interrelations holding between the logical systems determined by the above algebras. Zadanie „ Wdrożenie platformy Open Journal System dla czasopisma „ Bulletin of the Section of Logic” finansowane w ramach umowy 948/P-DUN/2016 ze środków Ministra Nauki i Szkolnictwa Wyższego przeznaczonych na działalność upowszechniającą naukę.
Balls into non-uniform bins
2014
Balls-into-bins games for uniform bins are widely used to model randomized load balancing strategies. Recently, balls-into-bins games have been analysed under the assumption that the selection probabilities for bins are not uniformly distributed. These new models are motivated by properties of many peer-to-peer (P2P) networks, which are not able to perfectly balance the load over the bins. While previous evaluations try to find strategies for uniform bins under non-uniform bin selection probabilities, this paper investigates heterogeneous bins, where the "capacities" of the bins might differ significantly. We show that heterogeneous environments can even help to distribute the load more eve…