Theories of orders on the set of words

Dietrich Kuske

Displaying similar documents to “Theories of orders on the set of words”

Towards parametrizing word equations

H. Abdulrab, P. Goralčík, G. S. Makanin (2010)

RAIRO - Theoretical Informatics and Applications

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Classically, in order to resolve an equation ≈ over a free monoid *, we reduce it by a suitable family $ℱ$ of substitutions to a family of equations ≈ , $f \in ℱ$ , each involving less variables than ≈ , and then combine solutions of ≈ into solutions of ≈ . The problem is to get $ℱ$ in a handy form. The method we propose consists in parametrizing the path traces in the so called associated to ≈ . We carry out such a parametrization in the case the prime equations in the graph involve at...

A Compositional Approach to Synchronize Two Dimensional Networks of Processors

Salvatore La Torre, Margherita Napoli, Mimmo Parente (2010)

RAIRO - Theoretical Informatics and Applications

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The problem of synchronizing a network of identical processors that work synchronously at discrete steps is studied. Processors are arranged as an array of rows and columns and can exchange each other only one bit of information. We give algorithms which synchronize square arrays of ( × ) processors and give some general constructions to synchronize arrays of ( × ) processors. Algorithms are given to synchronize in time , $n ⌈ log n ⌉$ , $n ⌈ \sqrt{n} ⌉$ and 2 a square array of ( × ) processors. Our...

Exponential convergence of quadrature for integral operators with Gevrey kernels

Alexey Chernov, Tobias von Petersdorff, Christoph Schwab (2011)

ESAIM: Mathematical Modelling and Numerical Analysis

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Galerkin discretizations of integral equations in $ℝ^{d}$ require the evaluation of integrals $I = \int_{S^{(1)}} \int_{S^{(2)}} g (x, y) d y d x$ where , are -simplices and has a singularity at = . We assume that is Gevrey smooth for $\neq$ and satisfies bounds for the derivatives which allow algebraic singularities at = . This holds for kernel functions commonly occurring in integral equations. We construct a family of quadrature rules $𝒬_{N}$ using function evaluations of which...