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A Note on Negative Tagging for Least Fixed-Point Formulae

Dilian Gurov, Bruce Kapron (2010)

RAIRO - Theoretical Informatics and Applications

Proof systems with sequents of the form U ⊢ Φ for proving validity of a propositional modal μ-calculus formula Φ over a set U of states in a given model usually handle fixed-point formulae through unfolding, thus allowing such formulae to reappear in a proof. Tagging is a technique originated by Winskel for annotating fixed-point formulae with information about the proof states at which these are unfolded. This information is used later in the proof to avoid unnecessary unfolding, without...

A note on the computational complexity of hierarchical overlapping clustering

Mirko Křivánek (1985)

Aplikace matematiky

In this paper the computational complexity of the problem of the approximation of a given dissimilarity measure on a finite set X by a k -ultrametric on X and by a Robinson dissimilarity measure on X is investigared. It is shown that the underlying decision problems are NP-complete.

A note on the hardness results for the labeled perfect matching problems in bipartite graphs

Jérôme Monnot (2008)

RAIRO - Operations Research

In this note, we strengthen the inapproximation bound of O(logn) for the labeled perfect matching problem established in J. Monnot, The Labeled perfect matching in bipartite graphs, Information Processing Letters96 (2005) 81–88, using a self improving operation in some hard instances. It is interesting to note that this self improving operation does not work for all instances. Moreover, based on this approach we deduce that the problem does not admit constant approximation algorithms for connected...

A note on the number of squares in a partial word with one hole

Francine Blanchet-Sadri, Robert Mercaş (2009)

RAIRO - Theoretical Informatics and Applications

A well known result of Fraenkel and Simpson states that the number of distinct squares in a word of length n is bounded by 2n since at each position there are at most two distinct squares whose last occurrence starts. In this paper, we investigate squares in partial words with one hole, or sequences over a finite alphabet that have a “do not know” symbol or “hole”. A square in a partial word over a given alphabet has the form uv where u is compatible with v, and consequently, such square is...

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