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Lower bounds for Las Vegas automata by information theory

Mika Hirvensalo, Sebastian Seibert (2003)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

We show that the size of a Las Vegas automaton and the size of a complete, minimal deterministic automaton accepting a regular language are polynomially related. More precisely, we show that if a regular language L is accepted by a Las Vegas automaton having r states such that the probability for a definite answer to occur is at least p , then r ≥ n p , where n is the number of the states of the minimal deterministic automaton accepting L . Earlier this result has been obtained in [2] by using a reduction...

Lower Bounds for Las Vegas Automata by Information Theory

Mika Hirvensalo, Sebastian Seibert (2010)

RAIRO - Theoretical Informatics and Applications

We show that the size of a Las Vegas automaton and the size of a complete, minimal deterministic automaton accepting a regular language are polynomially related. More precisely, we show that if a regular language L is accepted by a Las Vegas automaton having r states such that the probability for a definite answer to occur is at least p, then r ≥ np, where n is the number of the states of the minimal deterministic automaton accepting L. Earlier this result has been obtained in [2] by using a reduction...

Mathematical aspects of the theory of measures of fuzziness.

Doretta Vivona (1996)

Mathware and Soft Computing

After recalling the axiomatic concept of fuzziness measure, we define some fuzziness measures through Sugeno's and Choquet's integral. In particular, for the so-called homogeneous fuzziness measures we prove two representation theorems by means of the above integrals.

Maximal circular codes versus maximal codes

Yannick Guesnet (2001)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

We answer to a question of De Luca and Restivo whether there exists a circular code which is maximal as circular code and not as code.

Maximal circular codes versus maximal codes

Yannick Guesnet (2010)

RAIRO - Theoretical Informatics and Applications

We answer to a question of De Luca and Restivo whether there exists a circular code which is maximal as circular code and not as code.

Maximizing multi–information

Nihat Ay, Andreas Knauf (2006)

Kybernetika

Stochastic interdependence of a probability distribution on a product space is measured by its Kullback–Leibler distance from the exponential family of product distributions (called multi-information). Here we investigate low-dimensional exponential families that contain the maximizers of stochastic interdependence in their closure. Based on a detailed description of the structure of probability distributions with globally maximal multi-information we obtain our main result: The exponential family...

Mean mutual information and symmetry breaking for finite random fields

J. Buzzi, L. Zambotti (2012)

Annales de l'I.H.P. Probabilités et statistiques

G. Edelman, O. Sporns and G. Tononi have introduced the neural complexity of a family of random variables, defining it as a specific average of mutual information over subfamilies. We show that their choice of weights satisfies two natural properties, namely invariance under permutations and additivity, and we call any functional satisfying these two properties an intricacy. We classify all intricacies in terms of probability laws on the unit interval and study the growth rate of maximal intricacies...

Measures of fuzziness and operations with fuzzy sets.

Siegfried Gottwald, Ernest Czogala, Witold Pedrycz (1982)

Stochastica

We discuss the effects that the usual set theoretic and arithmetic operations with fuzzy sets and fuzzy numbers have with respect to the energies and entropies of the fuzzy sets connected and of the resulting fuzzy sets, and we also compare the entropies and energies of the results of several of those operations.

Measures of fuzziness based on t-norms.

Ronald R. Yager (1982)

Stochastica

We use the concept of t-norms and conorms to develop a pseudo metric and we then use this pseudo metric to define a class of measures of fuzziness associated with a fuzzy set. We investigate the properties of this class of measures of fuzziness.

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