Reduced languages as omega-generators

International audienceWe consider the following decision problem: “Is a rational omega-language generated by a code ?” Since 1994, the codes admit a characterization in terms of infinite words. We derive from this result the definition of a new class of languages, the reduced languages. A code is a reduced language but the converse does not hold. The idea is to “reduce" easy-to-obtain minimal omega-generators in order to obtain codes as omega-generators

Des codes pour engendrer des langages de mots infinis

This thesis deals with the languages of infinite words which are the ω-powers of a language of finite words. In particular, we focus on the open question : given a language L, does there exist an ω-code C such that C^ω = L^ω ? It is quite similar to the question deciding whether a submonoid of a free monoid is generated by a code.First, we study the set of relations satisfied by language L, i.e. the double factorizations of a word in L^∗ ∪ L^ω. We establish a necessary condition for that L^ω has a code or an ω-code generator. Next, we define the new class of languages where the set of relations is as simple as possible after codes : one-relation languages. For this class of languages, we characterize the languages L such that there exists a code or an ω-code C such that L^ω = C^ω, and we show that C is never a finite language. Finally, a characterization of codes concerning infinite words leads us to define reduced languages. We consider the properties of these languages as generators of languages of infinite words.Le sujet de cette thèse est l'étude des langages de mots infinis, en particulier les puissances infinies de langages de mots finis (puissance ω). Plus précisément, nous nous intéressons à la question ouverte suivante : étant donné un langage L, existe- t-il un ω-code C tel que C^ω = L^ω ? Cette question est l’analogue de celle pour la concaténation finie : un sous-monoïde d’un monoïde libre est-il engendré par un code ou non?Dans un premier temps, nous étudions l’ensemble des relateurs d’un langage L, c’est-`à-dire les couples de factorisations différentes d’un même mot de L^∗ ∪ ^Lω ; nous établissons une condition nécessaire pour que L^ω ait un code ou un ω-code générateur. Ensuite, nous définissons une nouvelle classe de langages : les langages à un relateur. Leurs ensemble de relateurs est le plus simple possible sans qu’ils soient des codes. Pour cette classe intéressante de langages, on caractérise les langages L tels qu’il existe un ω-code ou un code C tels que L^ω = C^ω. On montre que C ne peut pas être un langage fini. Enfin, une caractéisation des codes concernant les mots infinis nous amène à définir les langages réduits ; nous considérons les propriétés de ces langages en tant que générateurs de langages de mots infinis

ĐẶC ĐIỂM BIẾN ĐỘNG DÒNG CHẢY VÙNG VEN BỜ CHÂU THỔ SÔNG HỒNG - KẾT QUẢ NGHIÊN CỨU TỪ MÔ HÌNH 3D

This paper presents some results of three dimension (3D) modelling application to research characteristics of field current variation in the coastal area of Red River Delta. In the study, a 3D numerical model was set up with four vertical layers (s coordinate system). The open sea boundary conditions of hydrodynamics model have been obtained by NESTING method from the same l model for the larger marine region. Hydrodynamics model was calibrated and validated by measured data of water levels in Hon Dau National Hydrographic Station and data of currents in other sites (Ba Lat and Nam Trieu). In the studied results the temporal and spatial variation of total currents  and residual currents in the coastal area of Red River Delta are obtained, in which the different roles of tidal oscillations-tide currents, fresh water from river mouths, wind stress-gradient currents and density currents were recorded (the roles of wave induced currents are ignored).Bài viết này trình bày các kết quả áp dụng mô hình toán học 3 chiều (3D) để nghiên cứu đặc điểm biến động dòng chảy ở vùng ven bờ châu thổ sông Hồng. Trong nghiên cứu này, một mô hình 3 chiều đã được thiết lập với 4 lớp độ sâu (hệ tọa độ s). Số liệu đưa vào từ các biên mở phía biển có được thông qua sử dụng phương pháp lưới lồng (NESTING) cùng một mô hình tính rộng hơn ở phía ngoài. Mô hình đã được hiệu chỉnh kiểm chứng với số liệu đo mực nước tại Hòn Dáu và dòng chảy tại một số điểm (Ba Lạt, Nam Triệu) trong khu vực nghiên cứu. Các kết quả tính toán đã cho thấy các đặc điểm biến động theo không gian và thời gian của trường dòng chảy tổng hợp và dòng dư ở khu vực ven bờ châu thổ sông Hồng, trong đó đã chỉ ra các vai trò khác nhau của dao động mực nước - dòng triều, dòng chảy sông, trường gió - dòng gradien và dòng chảy mật độ (không tính đến vai trò của dòng chảy do sóng)

On the Performance of a Simple Approximation Algorithm for the Longest Path Problem

The longest path problem is known to be NP-hard. Moreover, they cannot be approximated within a constant ratio, unless ${\rm P=NP}$. The best known polynomial time approximation algorithms for this problem essentially find a path of length that is the logarithm of the optimum.In this paper we investigate the performance of an approximation algorithm for this problem in almost every case. We show that a simple algorithm, based on depth-first search, finds on almost every undirected graph $G=(V,E)$ a path of length more than $|V|-3\sqrt{|V| \log |V|}$ and so has performance ratio less than $1+4\sqrt{\log |V|/|V|}$.

Smart Shopping Assistant: A Multimedia and Social Media Augmented System with Mobile Devices to Enhance Customers’ Experience and Interaction

Multimedia, social media content, and interaction are common means to attract customers in shopping. However these features are not always fully available for customers when they go shopping in physical shopping centers. The authors propose Smart Shopping Assistant, a multimedia and social media augmented system on mobile devices to enhance users’ experience and interaction in shopping. Smart Shopping turns a regular mobile device into a special prism so that a customer can enjoy multimedia, get useful social media related to a product, give feedbacks or make actions on a product during shopping. The system is specified as a flexible framework to take advantages of different visual descriptors and web information extraction modules. Experimental results show that Smart Shopping can process and provide augmented data in a realtime-manner. Smart Shopping can be used to attract more customers and to build an online social community of customers to share their interests in shopping

Active fault-tolerance of the unmanned aerial vehicle automatic control systems

This paper presents an introductory overview of principles of the three-layer hierarchy of active fault-tolerance, providing, determination of the fault type with as many details as enough to get recoverable fault reason and failure toleration by flexible redundancy using; the conception of active fault-tolerant control in abnormal modes is described. Developed models and methods of a systematic approach to fault tolerance in the direction of the effective use of the signal, parametric and structural redundancies and selection of parrying tools. Performed experimental researches of the unmanned aerial vehicle (UAV) automatic control systems (ACS)

Reliability-Security in Wireless-Powered Cooperative Network with Friendly Jammer

n this paper, we study the Outage Probabil- ity (OP) and the Intercept Probability (IP) of Wireless- Powered Cooperative Networks (WPCNs) in the pres- ence of a malicious eavesdropper and a friendly jam- mer. We specifically present the system model and the power splitting Energy Harvesting (EH) architec- ture to increase system reliability and security. In ad- dition, we obtain exact analytical equations for the OP and IP. Asymptotic analysis in the low Signal-to-Jam Ratio (SJR) regimes expressed in integral-form expres- sions are provided to observe the lower bound of the IP. Finally, all derivations are validated by simulation results using the Monte Carlo method