A Group-theory Method to The Cycle Structures of Feedback Shift Registers

In this paper, we consider the cycle structures of feedback shift registers (FSRs). At the beginning, the cycle structures of two special classes of FSRs, pure circulating registers (PCRs) and pure summing registers (PSRs), are studied and it is proved that there are no other FSRs have the same cycle structure of an PCR (or PSR). Then, we regard $n$-stage FSRs as permutations over $2^n$ elements. According to the group theory, two permutations have the same cycle structure if and only if they are conjugate with each other. Since a conjugate of an FSR may no longer an FSR, it is interesting to consider the permutations that always transfer an FSR to an FSR. It is proved that there are exactly two such permutations, the identity mapping and the mapping that map every state to its dual. Furthermore, we prove that they are just the two permutations that transfer any maximum length FSR to an maximum length FSR

De Bruijn Sequences from Symmetric Shift Registers

We consider the symmetric Feedback Shift Registers (FSRs), especially a special class of symmetric FSRs (we call them scattered symmetric FSRs), and construct a large class of De Bruijn sequences from them. It is shown that, at least O(2^((n-6)(logn)/2)) De Bruijn sequences of order n can be constructed from just one n-stage scattered symmetric FSR. To generate the next bit in the De Bruijn sequence from the current state, it requires no more than 2n comparisons and n+1 FSR shifts. By further analyse the cycle structure of the scattered symmetric FSRs, other methods for constructing De Bruijn sequences are suggested

THE PERIODS OF THE SEQUENCES GENERATED BY SOME SYMMETRIC SHIFT REGISTERS

AbstractEk(x2,…, xn) is defined by Ek(a2,…, an) = 1 if and only if ∑i=2nai = k. We determine the periods of sequences generated by the shift registers with the feedback functions x1 + Ek(x2,…, xn) and x1 + Ek(x2,…, xn) + Ek+1(x2,…, xn) over the field GF(2)

De Bruijn Sequences from Joining Cycles of Nonlinear Feedback Shift Registers

De Bruijn sequences are a class of nonlinear recurring sequences that have wide applications in cryptography and modern communication systems. One main method for constructing them is to join the cycles of a feedback shift register (FSR) into a full cycle, which is called the cycle joining method. Jansen et al. (IEEE Trans on Information Theory 1991) proposed an algorithm for joining cycles of an arbitrary FSR. This classical algorithm is further studied in this paper. Motivated by their work, we propose a new algorithm for joining cycles, which doubles the efficiency of the classical cycle joining algorithm. Since both algorithms need FSRs that only generate short cycles, we also propose efficient ways to construct short-cycle FSRs. These FSRs are nonlinear and are easy to obtain. As a result, a large number of de Bruijn sequences are constructed from them. We explicitly determine the size of these de Bruijn sequences. Besides, we show a property of the pure circulating register, which is important for searching for short-cycle FSRs

Implémentation de méthodes d'intelligence artificielle pour le contrôle du procédé de projection thermique

Depuis sa création, la projection thermique ne cesse d étendre son champ d application en raison de ses potentialités à projeter des matériaux bien différents (métallique, céramique, plastique,...) sous des formes bien différentes aussi (poudre, fil, suspension, solution,...). Plusieurs types de procédés ont été développés afin de satisfaire les applications industrielles, par exemple, le procédé HVOF (High Velocity Oxygen Fuel), le procédé APS (Atmospheric Plasma Spraying), le procédé VLPPS (Very Low Pressure Plasma Spray). Parmi ces procédés, le procédé APS est aujourd hui bien implanté dans l industrie et en laboratoire réussissant à élaborer des revêtements de bonne qualité à coût intéressant. Néanmoins, cette technologie pâtit des incidences des instabilités du procédé sur la qualité du produit obtenu et souffre d un manque de compréhension des relations entre les paramètres opératoires et les caractéristiques des particules en vol.Pour rappel, pendant la projection APS, les phénomènes d instabilité du pied d arc, d érosion des électrodes, d instabilité des paramètres opératoires ne peuvent pas être complètement éliminés. Et, il est encore aujourd hui difficile de mesurer et de bien contrôler ces paramètres.Compte tenu des progrès réalisés sur les moyens de diagnostic qui peuvent être utilisés en milieu hostile (comme dans le cas de la projection APS), un contrôle efficace de ce procédé en boucle fermée peut être maintenant envisagé et requiert le développement d un système expert qui se compose des réseaux de neurones artificiels et de logique floue. Les réseaux de neurones artificiels sont développés dans plusieurs domaines d application et aussi maintenant au cas de la projection thermique. La logique floue quant à elle est une extension de la logique booléenne basée sur la théorie mathématique des ensembles flous. Nous nous sommes intéressés dans ce travail à bâtir le modèle de contrôle en ligne du procédé de projection basé sur des éléments d Intelligence Artificielle et à construire un émulateur qui reproduise aussi fidèlement que possible le comportement dynamique du procédé.Since its creation, the thermal spraying continuously expands its application scope because of its potential to project very different materials (metal, ceramic, plastic ...) as well as different forms (powder, wire, suspension, solution ...). Several types of methods have been developed to meet industrial applications, for example, the process HVOF (High Velocity Oxygen Fuel), the process APS (Atmospheric Plasma Spraying), the process VLPPS (Very Low Pressure Plasma Spray). Among these methods, the APS process is now well established in the industry and laboratory for successfully developing coatings with good quality but low cost. However, this technology suffers from the instability effect of the process on the obtained product quality and endures a lack of understanding of the relationship between the operating parameters and the characteristics of in-flight particles.As a reminder, during the projection APS, the arc foot instability phenomena, the electrode erosion, the instability of the operating parameters cannot be completely eliminated. Further, it is still difficult to measure and control these parameters well. With the developing technology of diagnostic tools that can be used in a hostile environment (as in the case of APS process), an effective control of APS process in closed-loop can be considered and requires the development of an expert system consisting of artificial neural networks and fuzzy logic controlling. The artificial neural networks have been developed in several application fields and now also to plasma spraying process. Fuzzy logic controlling is an extension of Boolean logic based on the mathematical theory of fuzzy sets.We are interested in this work to build an on-line control model for the APS process based on the elements of artificial intelligence and to build an emulator that replicates as closely as possible the dynamic behavior of the process. Further, the artificial neural networks will be combined with the emulator for constituting a big system who can monitor the process and also can automatically carry out modification action. The system then will be tested off-line, the time response will be discussed.BELFORT-UTBM-SEVENANS (900942101) / SudocSudocFranceF