Search results for "Iterated logarithm"

showing 4 items of 4 documents

First-order expressibility of languages with neutral letters or: The Crane Beach conjecture

2005

A language L over an alphabet A is said to have a neutral letter if there is a letter [email protected]?A such that inserting or deleting e's from any word in A^* does not change its membership or non-membership in L. The presence of a neutral letter affects the definability of a language in first-order logic. It was conjectured that it renders all numerical predicates apart from the order predicate useless, i.e., that if a language L with a neutral letter is not definable in first-order logic with linear order, then it is not definable in first-order logic with any set N of numerical predicates. Named after the location of its first, flawed, proof this conjecture is called the Crane Beach …

Discrete mathematicsConjectureComputer Networks and CommunicationsApplied MathematicsFirst orderNumerical predicatesPredicate (grammar)Theoretical Computer ScienceFirst-order logicIterated logarithmCombinatoricsComputational Theory and MathematicsRegular languageDatabase theoryCircuit complexityFirst-order logicCircuit uniformityMathematicsJournal of Computer and System Sciences
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Law of the Iterated Logarithm

2020

For sums of independent random variables we already know two limit theorems: the law of large numbers and the central limit theorem. The law of large numbers describes for large \(n\in \mathbb{N}\) the typical behavior, or average value behavior, of sums of n random variables. On the other hand, the central limit theorem quantifies the typical fluctuations about this average value.

Discrete mathematicsIterated logarithmNatural logarithm of 2LogarithmLaw of large numbersLaw of the iterated logarithmLimit (mathematics)Random variableMathematicsCentral limit theorem
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Radial growth of solutions to the poisson equation

2001

We establish a radial growth estimate of the type of the iterated law of the logarithm for solutions to the Poisson equation in the unit ball.

Laplace's equationUnit spheresymbols.namesakeUniqueness theorem for Poisson's equationLogarithmIterated functionDiscrete Poisson equationMathematical analysissymbolsLaw of the iterated logarithmGeneral MedicinePoisson's equationMathematicsComplex Variables, Theory and Application: An International Journal
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The Crane Beach Conjecture

2002

A language L over an alphabet A is said to have a neutral letter if there is a letter e/spl isin/A such that inserting or deleting e's from any word in A* does not change its membership (or non-membership) in L. The presence of a neutral letter affects the definability of a language in first-order logic. It was conjectured that it renders all numerical predicates apart from the order predicate useless, i.e., that if a language L with a neutral letter is not definable in first-order logic with linear order then it is not definable in first-order. Logic with any set /spl Nscr/ of numerical predicates. We investigate this conjecture in detail, showing that it fails already for /spl Nscr/={+, *…

Predicate logicDiscrete mathematicsIterated logarithmConjectureComputational complexity theoryDescription logicComputer Science::Logic in Computer ScienceComputer Science::Software EngineeringBinary numberSigmaPredicate (grammar)MathematicsProceedings 16th Annual IEEE Symposium on Logic in Computer Science
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