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Acceleration of Le Bail fitting method on parallel platforms

Mařík, Ondřej, Šimeček, Ivan (2015)

Programs and Algorithms of Numerical Mathematics

Le Bail fitting method is procedure used in the applied crystallography mainly during the crystal structure determination. As in many other applications, there is a need for a great performance and short execution time. In this paper, we describe utilization of parallel computing for mathematical operations used in Le Bail fitting. We present an algorithm implementing this method with highlighted possible approaches to its aforementioned parallelization. Then, we propose a sample parallel version...

An intrinsically non minimal-time Minsky-like 6-states solution to the Firing Squad synchronization problem

Jean-Baptiste Yunès (2008)

RAIRO - Theoretical Informatics and Applications

Here is presented a 6-states non minimal-time solution which is intrinsically Minsky-like and solves the three following problems: unrestricted version on a line, with one initiator at each end of a line and the problem on a ring. We also give a complete proof of correctness of our solution, which was never done in a publication for Minsky's solutions.

Computing ϵ-Free NFA from Regular Expressions in O(n log2(n)) Time

Christian Hagenah, Anca Muscholl (2010)

RAIRO - Theoretical Informatics and Applications

The standard procedure to transform a regular expression of size n to an ϵ-free nondeterministic finite automaton yields automata with O(n) states and O(n2) transitions. For a long time this was supposed to be also the lower bound, but a result by Hromkovic et al. showed how to build an ϵ-free NFA with only O(n log2(n)) transitions. The current lower bound on the number of transitions is Ω(n log(n)). A rough running time estimation for the common follow sets (CFS) construction proposed...

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