A Fast Algorithm Finding the Shortest Reset Words

In this paper we present a new fast algorithm finding minimal reset words for finite synchronizing automata. The problem is know to be computationally hard, and our algorithm is exponential. Yet, it is faster than the algorithms used so far and it works well in practice. The main idea is to use a bidirectional BFS and radix (Patricia) tries to store and compare resulted subsets. We give both theoretical and practical arguments showing that the branching factor is reduced efficiently. As a practical test we perform an experimental study of the length of the shortest reset word for random automata with $n$ states and 2 input letters. We follow Skvorsov and Tipikin, who have performed such a study using a SAT solver and considering automata up to $n=100$ states. With our algorithm we are able to consider much larger sample of automata with up to $n=300$ states. In particular, we obtain a new more precise estimation of the expected length of the shortest reset word $\approx 2.5\sqrt{n-5}$.Comment: COCOON 2013. The final publication is available at http://link.springer.com/chapter/10.1007%2F978-3-642-38768-5_1

Study of random w-trees and automaton synchronization

En aquest treball s'han investigat numèricament i analíticament les propietats de sincronització de paraules repetides en autòmats finits deterministes. Es presenta un algorisme polinomi O(n^2) per trobar paraules curtes de sincronització basades en arbres w. L'algorisme és capaç de trobar paraules sincronitzadores de longitud proporcional a (n log(n))^0.5 amb autòmats de mida de fins a uns quants centenars de milers d'estats. També es presenten resultats experimentals sobre l'alçada dels arbres w que mostren que l'alçada mitjana de l'arbre és de O((n/k)^0.5). A més, en aquest estudi es porta a terme el modelatge del procés de sincronització aleatori de DFA per cadenes de Markov. També es presenten tres estimacions diferents justificades experimentalment per a la longitud mitjana de la paraula de sincronització més curta, que indiquen que la longitud de la paraula de reinici més curta és proporcional a l'arrel quadrada de la mida de l'autòmat.En este trabajo se investigaron numérica y analíticamente las propiedades de sincronización de palabras repetidas en autómatas finitos deterministas. Se presenta un algoritmo polinomial O (n ^ 2) para encontrar palabras sincronizadas cortas basadas en árboles w. El algoritmo es capaz de encontrar palabras de sincronización de longitud proporcional a (n log(n))^0.5 con autómatas de tamaño de unos pocos cientos de miles de estados. También se presentan resultados experimentales sobre la altura de los árboles w los cuales muestran que la altura media de los árboles es de O((n/k)^0.5). Además, en este estudio se lleva a cabo el modelado del proceso de sincronización aleatoria DFA por cadenas de Markov. También se presentan tres estimaciones diferentes justificadas experimentalmente para la longitud media de la palabra de sincronización más corta, lo que indica que la longitud de la palabra de reinicio más corta es proporcional a la raíz cuadrada del tamaño del autómata.The synchronization properties of repeated words on deterministic finite automata were investigated numerically and analytically in this work. A polynomial O(n^2) algorithm for finding short synchronizing words based on w-trees is presented. The algorithm is capable of finding synchronizing words of length proportional to (n log(n))^0.5 with automata of size up to a few hundred thousand states. Experimental results on the height of w-trees is also presented showing that the mean tree height is of O((n/k)^0.5). Furthermore, the modeling of the random DFA synchronization process by Markov chains is carried out in this study. Three different experimentally justified estimates for the mean shortest synchronizing word length are presented as well indicating that the shortest resetting word length is proportional to the square root of the automaton size

Manufacturing Logistics and Packaging Management Using RFID

none2The chapter is centred on the analysis of internal flow traceability of goods (products and/or packaging) along the supply chain by an Indoor Positioning System (IPS) based on Radio Frequency IDentification (RFID) technology. A typical supply chain is an end-to-end process with the main purpose of production, transportation, and distribution of products. It is relative to the products’ movements from the supplier to the manufacturer, distributor, retailer and finally to the end consumer. Moreover, a supply chain is a complex amalgam of parties that require coordination, collaboration, and information exchange among them to increase productivity and efficiency [1, 2]. A supply chain is made up of people, activities, and resources involved in moving products from suppliers to customers and information from customers to suppliers. For this reason, the traceability of logistics flows (physical and information) is a very important issue for the definition and design of manufacturing processes, improvement of layout and increase of security in work areas. European Parliament (Regulation (EC) No. 178/2002) [3] makes it compulsory to trace goods and record all steps, used materials, manufacturing processes, etc. during the entire life cycle of a product [4]. According to the European Parliament, companies recognize the need and importance of tracing materials in indoor environments. Traditionally, the traceability system is performed through the asynchronous fulfilment of checkpoints (i.e. doorways) by materials. In such cases, the tracking is manual, executed by operators. Often companies are not aware of the inefficiencies due to these systems of traceability such as low precision and accuracy in measurements (i.e. no information between doorways), more time spent by operators and costs (due to the full-effort of operators who have to trace target positions and movements). According to [5] every day millions of transport units (cases, boxes, pallets, and containers) are managed worldwide with limited or even with lack of knowledge regarding their status in real-time. In order to overcome the lack of data due to traceability, automatic identification procedures (Auto-ID) could be a solution. They have become very popular in many service industries, purchasing and distribution logistics, manufacturing companies and material flow systems. Automatic identification procedures provide information about people, vehicles, goods, and products in transit within the company [6]. It is possible to note several advantages using an automatic identification system such as the reduction of theft, increase of security during the transport and distribution of assets, and increase of knowledge of objects’ position in real-time. Automatic identification procedures can also be applied to packaging products, instead of to each item contained in the package. Packaging is becoming the cornerstone of processing activities [7]. Sometimes products are very expensive and packages contain important and critical goods (for example dangerous or explosive materials) and the tracking of goods – and packaging in particular – is a critical function. The main advantage of automatic system application to packages is the possibility to map the path of all items contained into the packages and to find out their real-time position. The installation of automatic systems in packages allows costs and time to be reduced (by installing, for example, the tag directly on the package instead of on each product contained inside the package). The purpose of the chapter is to provide an innovative automatic solution for the traceability of everything that moves within a company, in order to simplify and improve the process of logistics flow traceability and logistics optimization. The chapter deals with experimental research that consists of several tests, static and dynamic, tracing the position (static) and movements (dynamic) of targets (e.g. people, vehicles, objects) in indoor environments. In order to identify the best system to use in the real-time traceability of products, the authors have chosen Real Time Location Systems (RTLSs) and, in particular, the Indoor Positioning Systems (IPSs) based on Radio Frequency IDentification (RFID) technology. The authors discuss the RFID based system using UWB technology, both in terms of design of the system and real applications. The chapter is organized as follows: Section 2 briefly describes IPS systems, looking in more depth at RFID technology. After that the experimental research with the relative results and discussion are described in Section 3. Section 4 presents an analysis of RFID traceability systems applied to packaging. Conclusions and further research are discussed in Section 5.mixedREGATTIERI A.; SANTARELLI GREGATTIERI A.; SANTARELLI

Adaptive locomotion of snake-like robots

Adaptive locomotion for multi-robot organisms is a huge challenge in modern robotics. The complexity grows fast with the number of degrees of freedom (DOFs) of a robot. A snake like organism structure usually consists of many DOFs and is hence restricted in their motion capabilities. In this theses, an adaptive gait algorithm for avoiding of obstacles should be analyzed by using techniques of coupled oscillators. The simulation in MATLAB as well as tests on a real snake robot will be done in this work. In the MATLAB simulation we could see the principle of adaptive snake-like locomotion as it should be. As well we could analyse fitting functions for the oszillator in the Central Pattern Generator. On the real snake robot we had to take the theoretical foundations and adapt them to make them work on real-time operating system. It was faszinating to work on all difficulties be communication, configuration, designing or programming. And finally we saw the robot crawl arround obstacles, controlled by the equations we developed. It would be great to see our work live on in projects like SYMBRION and REPLICATOR