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.

Discrete mathematicsClassical mechanicsMathematics::ProbabilityPlane (geometry)Quantum walkMathematics
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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.

Discrete mathematicsCode (set theory)v-variable fractalsApplied MathematicsGeneral MathematicsProbability (math.PR)ta111Dynamical Systems (math.DS)self-similar setsTree (descriptive set theory)Box countingFractalIterated function systemMathematics - Classical Analysis and ODEsHausdorff dimensionClassical Analysis and ODEs (math.CA)FOS: MathematicsAffine transformationMathematics - Dynamical Systems28A80 60D05 37H99RandomnessMathematics - ProbabilityMathematics
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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.

Discrete mathematicsComputer Science::Computer Science and Game TheoryGeneral Computer ScienceQuantum pseudo-telepathyGeneralizationSymmetric gameComputingMilieux_PERSONALCOMPUTINGCombinatorial game theoryTheoryofComputation_GENERALSymmetric probability distributionTheoretical Computer ScienceSimple (abstract algebra)Quantum worldMathematical economicsQuantumMathematicsTheoretical Computer Science
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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].

Discrete mathematicsDensity matrixComputer Science::Information RetrievalProbability of errorGrover's algorithmMatrix normSearch problemQuantum algorithmQuantum search algorithmComputer Science::DatabasesMathematics
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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…

Discrete mathematicsDiscretizationLearning automataAbsorbing CPAComputer scienceEstimatorMonotonic functionVDP::Technology: 500::Information and communication technology: 550Mathematical proofFormal proofCPAArbitrarily largeArtificial Intelligenceε-optimalityMartingale (probability theory)Pursuit algorithmsAlgorithm
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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.

Discrete mathematicsHardware_MEMORYSTRUCTURESKolmogorov complexityLogarithmSublinear functionKolmogorov structure functionChain rule for Kolmogorov complexityOpen problemInductive probabilityInductive reasoningMathematics
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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.

Discrete mathematicsHigh probabilityProbabilistic finite automataComputer scienceProbabilistic automaton
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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…

Discrete mathematicsIndicative conditionalcenteringSettore MAT/06 - Probabilita' E Statistica Matematica05 social sciencesClassical logicConditional probabilityInference02 engineering and technologyCoherence (philosophical gambling strategy)p-entailmentn-conditional event050105 experimental psychologycoherenceLogical biconditionalp-validity0202 electrical engineering electronic engineering information engineeringbiconditional event020201 artificial intelligence & image processing0501 psychology and cognitive sciencesProbabilistic analysis of algorithmsArithmeticMathematicsEvent (probability theory)Conditional
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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.

Discrete mathematicsLogicprobabilityconsequence relationCumulative distribution functionPhilosophy03G20the infinite-valued standard Łukasiewicz algebracumulative distribution functionŁukasiewicz logic06D3060A05MathematicsBulletin of the Section of Logic
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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…

Discrete mathematicsMathematical optimizationComputational complexity theoryComputer Networks and CommunicationsComputer scienceDistributed computingAstrophysics::Cosmology and Extragalactic AstrophysicsPhysics::Data Analysis; Statistics and ProbabilityLoad balancing (computing)BinTheoretical Computer ScienceLoad managementCapacity planningArtificial IntelligenceHardware and ArchitectureTheoryofComputation_ANALYSISOFALGORITHMSANDPROBLEMCOMPLEXITYBounded functionBall (bearing)Resource allocationHardware_ARITHMETICANDLOGICSTRUCTURESGame theorySoftwareMathematicsMathematicsofComputing_DISCRETEMATHEMATICS2010 IEEE International Symposium on Parallel & Distributed Processing (IPDPS)
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