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Titlebook: Mathematical Foundations of Computer Science 2003; 28th International S Branislav Rovan,Peter Vojtáš Conference proceedings 2003 Springer-V

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https://doi.org/10.1007/b11836algorithms; combinatorial optimization; complexity; computer; computer science; formal method; logic; mathe
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On Optimal Merging Networksused. For other cases where . ≤ 4, the optimality of Batcher’s (.,.)-merging networks has been proved. So we can conclude that Batcher’s odd-even merge yields optimal (.,.)-merging networks for every . ≤ 4 and for every .. The crucial part of the proof is characterizing the structure of optimal (2,.)-merging networks.
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,-Unification Is NEXPTIME-Decidabletative idempotent operator ‘+’, possibly admitting a unit element .. We formulate the problem as a particular class of set constraints, and propose a method for solving it by using the dag automata introduced by W. Charatonik, that we enrich with labels for our purposes. .(.).-unification is thus shown to be in NEXPTIME.
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On the Length of the Minimum Solution of Word Equations in One Variablesponding variable occurrences in . and .. By introducing the notion of difference, the proof is obtained from Fine and Wilf’s theorem. As a corollary, it implies that the length of the minimum solution is less than . = ∣ . ∣ + ∣ . ∣.
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Inferring Strings from Graphs and Arraysrms of string inference. Finally, we consider the problem of finding a string . of a minimal size alphabet, such that the . (.) of . is identical to a given permutation .=..,...,.. of integers 1,...,.. Each of our three algorithms solving the above problems runs in linear time with respect to the input size.
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Faster Algorithms for ,-Medians in Treess paper we consider the case when the graph is a tree. We show that this problem can be solved in time . for the following cases: (i) directed trees (and any fixed .), (ii) balanced undirected trees, and (iii) undirected trees with .=3.
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Periodicity and Transitivity for Cellular Automata in Besicovitch Topologiesstems obtained using Kolmogorov complexity. We also prove that every CA (in Besicovitch topology) either has a unique fixed point or a countable set of periodic points. This result underlines that CA have a great degree of stability and may be considered a further step towards the understanding of CA periodic behavior.
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