Discrete Event Systems in Dioid Algebra and Conventional Algebra


Book Description

This book concerns the use of dioid algebra as (max, +) algebra to treat the synchronization of tasks expressed by the maximum of the ends of the tasks conditioning the beginning of another task – a criterion of linear programming. A classical example is the departure time of a train which should wait for the arrival of other trains in order to allow for the changeover of passengers. The content focuses on the modeling of a class of dynamic systems usually called “discrete event systems” where the timing of the events is crucial. Events are viewed as sudden changes in a process which is, essentially, a man-made system, such as automated manufacturing lines or transportation systems. Its main advantage is its formalism which allows us to clearly describe complex notions and the possibilities to transpose theoretical results between dioids and practical applications.




Analysis and Optimization of Systems


Book Description

INRIA, Institut National de Recherche en Informatique et en Automatique




European Control Conference 1991


Book Description

Proceedings of the European Control Conference 1991, July 2-5, 1991, Grenoble, France




Formal Methods in Manufacturing


Book Description

Illustrated with real-life manufacturing examples, Formal Methods in Manufacturing provides state-of-the-art solutions to common problems in manufacturing systems. Assuming some knowledge of discrete event systems theory, the book first delivers a detailed introduction to the most important formalisms used for the modeling, analysis, and control of manufacturing systems (including Petri nets, automata, and max-plus algebra), explaining the advantages of each formal method. It then employs the different formalisms to solve specific problems taken from today’s industrial world, such as modeling and simulation, supervisory control (including deadlock prevention) in a distributed and/or decentralized environment, performance evaluation (including scheduling and optimization), fault diagnosis and diagnosability analysis, and reconfiguration. Containing chapters written by leading experts in their respective fields, Formal Methods in Manufacturing helps researchers and application engineers handle fundamental principles and deal with typical quality goals in the design and operation of manufacturing systems.




A Guide to the Literature on Semirings and their Applications in Mathematics and Information Sciences


Book Description

This volume presents a short guide to the extensive literature concerning semir ings along with a complete bibliography. The literature has been created over many years, in variety of languages, by authors representing different schools of mathematics and working in various related fields. In many instances the terminology used is not universal, which further compounds the difficulty of locating pertinent sources even in this age of the Internet and electronic dis semination of research results. So far there has been no single reference that could guide the interested scholar or student to the relevant publications. This book is an attempt to fill this gap. My interest in the theory of semirings began in the early sixties, when to gether with Bogdan W ~glorz I tried to investigate some algebraic aspects of compactifications of topological spaces, semirings of semicontinuous functions, and the general ideal theory for special semirings. (Unfortunately, local alge braists in Poland told me at that time that there was nothing interesting in investigating semiring theory because ring theory was still being developed). However, some time later we became aware of some similar investigations hav ing already been done. The theory of semirings has remained "my first love" ever since, and I have been interested in the results in this field that have been appearing in literature (even though I have not been active in this area myself).




Kybernetika


Book Description




Semirings and Affine Equations over Them


Book Description

Semiring theory stands with a foot in each of two mathematical domains. The first being abstract algebra and the other the fields of applied mathematics such as optimization theory, the theory of discrete-event dynamical systems, automata theory, and formal language theory, as well as from the allied areas of theoretical computer science and theoretical physics. Most important applications of semiring theory in these areas turn out to revolve around the problem of finding the equalizer of a pair of affine maps between two semimodules. In this volume, we chart the state of the art on solving this problem, and present many specific cases of applications. This book is essentially the third part of a trilogy, along with Semirings and their Applications, and Power Algebras over Semirings, both written by the same author and published by Kluwer Academic Publishers in 1999. While each book can be read independently of the others, to get the full force of the theory and applications one should have access to all three. This work will be of interest to academic and industrial researchers and graduate students. The intent of the book is to bring the applications to the attention of the abstract mathematicians and to make the abstract mathematics available to those who are using these tools in an ad-hoc manner without realizing the full force of the theory.




Hardware/Software Co-Design and Co-Verification


Book Description

Co-Design is the set of emerging techniques which allows for the simultaneous design of Hardware and Software. In many cases where the application is very demanding in terms of various performances (time, surface, power consumption), trade-offs between dedicated hardware and dedicated software are becoming increasingly difficult to decide upon in the early stages of a design. Verification techniques - such as simulation or proof techniques - that have proven necessary in the hardware design must be dramatically adapted to the simultaneous verification of Software and Hardware. Describing the latest tools available for both Co-Design and Co-Verification of systems, Hardware/Software Co-Design and Co-Verification offers a complete look at this evolving set of procedures for CAD environments. The book considers all trade-offs that have to be made when co-designing a system. Several models are presented for determining the optimum solution to any co-design problem, including partitioning, architecture synthesis and code generation. When deciding on trade-offs, one of the main factors to be considered is the flow of communication, especially to and from the outside world. This involves the modeling of communication protocols. An approach to the synthesis of interface circuits in the context of co-design is presented. Other chapters present a co-design oriented flexible component data-base and retrieval methods; a case study of an ethernet bridge, designed using LOTOS and co-design methodologies and finally a programmable user interface based on monitors. Hardware/Software Co-Design and Co-Verification will help designers and researchers to understand these latest techniques in system design and as such will be of interest to all involved in embedded system design.




Handbook of Linear Algebra


Book Description

The Handbook of Linear Algebra provides comprehensive coverage of linear algebra concepts, applications, and computational software packages in an easy-to-use handbook format. The esteemed international contributors guide you from the very elementary aspects of the subject to the frontiers of current research. The book features an accessibl