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Defect theorem in the plane

Włodzimierz Moczurad (2007)

RAIRO - Theoretical Informatics and Applications

We consider the defect theorem in the context of labelled polyominoes, i.e., two-dimensional figures. The classical version of this property states that if a set of n words is not a code then the words can be expressed as a product of at most n - 1 words, the smaller set being a code. We survey several two-dimensional extensions exhibiting the boundaries where the theorem fails. In particular, we establish the defect property in the case of three dominoes (n × 1 or 1 × n rectangles).

Definition of Flat Poset and Existence Theorems for Recursive Call

Kazuhisa Ishida, Yasunari Shidama, Adam Grabowski (2014)

Formalized Mathematics

This text includes the definition and basic notions of product of posets, chain-complete and flat posets, flattening operation, and the existence theorems of recursive call using the flattening operator. First part of the article, devoted to product and flat posets has a purely mathematical quality. Definition 3 allows to construct a flat poset from arbitrary non-empty set [12] in order to provide formal apparatus which eanbles to work with recursive calls within the Mizar langauge. To achieve this...

Deformed fuzzy automata for the Text Error Correction Problem.

F. Javier Echanobe Arias, José Ramón Garitagoitia, José Ramón González de Mendívil, José Javier Astráin (2000)

Mathware and Soft Computing

A fuzzy method for the text error correction problem is introduced. The method is able to handle insert, delete and substitution errors. Moreover, it uses the measurement level output that an Isolated Character Classifier can provide. The method is based on a Deformed System, in particular, a deformed fuzzy automaton is defined to model the possible errors in the words of the texts. Experimental results show good performance in correcting the three types of errors.

Denotational aspects of untyped normalization by evaluation

Andrzej Filinski, Henning Korsholm Rohde (2005)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

We show that the standard normalization-by-evaluation construction for the simply-typed λ β η -calculus has a natural counterpart for the untyped λ β -calculus, with the central type-indexed logical relation replaced by a “recursively defined” invariant relation, in the style of Pitts. In fact, the construction can be seen as generalizing a computational-adequacy argument for an untyped, call-by-name language to normalization instead of evaluation.In the untyped setting, not all terms have normal forms,...

Denotational aspects of untyped normalization by evaluation

Andrzej Filinski, Henning Korsholm Rohde (2010)

RAIRO - Theoretical Informatics and Applications

We show that the standard normalization-by-evaluation construction for the simply-typed λβη-calculus has a natural counterpart for the untyped λβ-calculus, with the central type-indexed logical relation replaced by a “recursively defined” invariant relation, in the style of Pitts. In fact, the construction can be seen as generalizing a computational-adequacy argument for an untyped, call-by-name language to normalization instead of evaluation.In the untyped setting, not all terms have normal...

Denotational semantics of languages with fuzzy data.

Daniel Sánchez Alvarez, Antonio F. Gómez Skarmeta (2000)

Mathware and Soft Computing

The denotational semantics of a programming language which manages fuzzy data is presented. The introduction of blocks poses problems regarding transmission, both for the degree at which the work is carried out and for triangular operations necessary for the evaluation of the degrees of the fuzzy data. We propose some solutions. The possibility of defining linguistic variables is provided.

Density estimation with quadratic loss: a confidence intervals method

Pierre Alquier (2008)

ESAIM: Probability and Statistics

We propose a feature selection method for density estimation with quadratic loss. This method relies on the study of unidimensional approximation models and on the definition of confidence regions for the density thanks to these models. It is quite general and includes cases of interest like detection of relevant wavelets coefficients or selection of support vectors in SVM. In the general case, we prove that every selected feature actually improves the performance of the estimator. In the case...

Depth lower bounds for monotone semi-unbounded fan-in circuits

Jan Johannsen (2001)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

The depth hierarchy results for monotone circuits of Raz and McKenzie [5] are extended to the case of monotone circuits of semi-unbounded fan-in. It follows that the inclusions N C i S A C i A C i are proper in the monotone setting, for every i 1 .

Depth Lower Bounds for Monotone Semi-Unbounded Fan-in Circuits

Jan Johannsen (2010)

RAIRO - Theoretical Informatics and Applications

The depth hierarchy results for monotone circuits of Raz and McKenzie [5] are extended to the case of monotone circuits of semi-unbounded fan-in. It follows that the inclusions NCi ⊆ SACi ⊆ ACi are proper in the monotone setting, for every i ≥ 1.

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