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Comparing the succinctness of monadic query languages over finite trees

Martin Grohe, Nicole Schweikardt (2004)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

We study the succinctness of monadic second-order logic and a variety of monadic fixed point logics on trees. All these languages are known to have the same expressive power on trees, but some can express the same queries much more succinctly than others. For example, we show that, under some complexity theoretic assumption, monadic second-order logic is non-elementarily more succinct than monadic least fixed point logic, which in turn is non-elementarily more succinct than monadic datalog. Succinctness...

Comparing the succinctness of monadic query languages over finite trees

Martin Grohe, Nicole Schweikardt (2010)

RAIRO - Theoretical Informatics and Applications

We study the succinctness of monadic second-order logic and a variety of monadic fixed point logics on trees. All these languages are known to have the same expressive power on trees, but some can express the same queries much more succinctly than others. For example, we show that, under some complexity theoretic assumption, monadic second-order logic is non-elementarily more succinct than monadic least fixed point logic, which in turn is non-elementarily more succinct than monadic datalog.
Succinctness...

Comparison of supervised learning methods for spike time coding in spiking neural networks

Andrzej Kasiński, Filip Ponulak (2006)

International Journal of Applied Mathematics and Computer Science

In this review we focus our attention on supervised learning methods for spike time coding in Spiking Neural Networks (SNNs). This study is motivated by recent experimental results regarding information coding in biological neural systems, which suggest that precise timing of individual spikes may be essential for efficient computation in the brain. We are concerned with the fundamental question: What paradigms of neural temporal coding can be implemented with the recent learning methods? In order...

Comparison of two methods for approximation of probability distributions with prescribed marginals

Albert Pérez, Milan Studený (2007)

Kybernetika

Let P be a discrete multidimensional probability distribution over a finite set of variables N which is only partially specified by the requirement that it has prescribed given marginals { P A ; A ∈ 𝒮 } , where 𝒮 is a class of subsets of N with ⋃ 𝒮 = N . The paper deals with the problem of approximating P on the basis of those given marginals. The divergence of an approximation P ^ from P is measured by the relative entropy H ( P | P ^ ) . Two methods for approximating P are compared. One of them uses formerly introduced concept of...

Compatibility relations on codes and free monoids

Tomi Kärki (2008)

RAIRO - Theoretical Informatics and Applications

A compatibility relation on letters induces a reflexive and symmetric relation on words of equal length. We consider these word relations with respect to the theory of variable length codes and free monoids. We define an (R,S)-code and an (R,S)-free monoid for arbitrary word relations R and S. Modified Sardinas-Patterson algorithm is presented for testing whether finite sets of words are (R,S)-codes. Coding capabilities of relational codes are measured algorithmically by finding minimal and maximal relations....

Completing an uncertainty criterion of classification.

Joaquín Abellán (2005)

Mathware and Soft Computing

We present a variation of a method of classification based in uncertainty on credal set. Similarly to its origin it use the imprecise Dirichlet model to create the credal set and the same uncertainty measures. It take into account sets of two variables to reduce the uncertainty and to seek the direct relations between the variables in the data base and the variable to be classified. The success are equivalent to the success of the first method except in those where there are a direct relations between...

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