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Synchronization and linearity: an algebra for discrete event systems
, 2001
"... The first edition of this book was published in 1992 by Wiley (ISBN 0 471 93609 X). Since this book is now out of print, and to answer the request of several colleagues, the authors have decided to make it available freely on the Web, while retaining the copyright, for the benefit of the scientific ..."
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Cited by 279 (10 self)
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The first edition of this book was published in 1992 by Wiley (ISBN 0 471 93609 X). Since this book is now out of print, and to answer the request of several colleagues, the authors have decided to make it available freely on the Web, while retaining the copyright, for the benefit of the scientific community. Copyright Statement This electronic document is in PDF format. One needs Acrobat Reader (available freely for most platforms from the Adobe web site) to benefit from the full interactive machinery: using the package hyperref by Sebastian Rahtz, the table of contents and all LATEX crossreferences are automatically converted into clickable hyperlinks, bookmarks are generated automatically, etc.. So, do not hesitate to click on references to equation or section numbers, on items of thetableofcontents and of the index, etc.. One may freely use and print this document for one’s own purpose or even distribute it freely, but not commercially, provided it is distributed in its entirety and without modifications, including this preface and copyright statement. Any use of thecontents should be acknowledged according to the standard scientific practice. The
Minimal (max, +) realization of convex sequences
 SIAM JOURNAL ON CONTROL AND OPTIMIZATION
, 1998
"... We show that the minimal dimension of a linear realization over the (max,+) semiring of a convex sequence is equal to the minimal size of a decomposition of the sequence as a supremum of discrete affine maps. The minimaldimensional realization of any convex realizable sequence can thus be found in ..."
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Cited by 16 (5 self)
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We show that the minimal dimension of a linear realization over the (max,+) semiring of a convex sequence is equal to the minimal size of a decomposition of the sequence as a supremum of discrete affine maps. The minimaldimensional realization of any convex realizable sequence can thus be found in linear time. The result is based on a bound in terms of minors of the Hankel matrix.
On the Boolean Minimal Realization Problem in the MaxPlus Algebra
, 1998
"... One of the open problems in the maxplusalgebraic system theory for discrete event systems is the minimal realization problem. In this paper we present some results in connection with the minimal realization problem in the maxplus algebra. First we characterize the minimal system order of a maxli ..."
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Cited by 10 (7 self)
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One of the open problems in the maxplusalgebraic system theory for discrete event systems is the minimal realization problem. In this paper we present some results in connection with the minimal realization problem in the maxplus algebra. First we characterize the minimal system order of a maxlinear discrete event system. We also introduce a canonical representation of the impulse response of a maxlinear discrete event system. Next we consider a simpli#ed version of the general minimal realization problem: the boolean minimal realization problem, i.e., we consider models in which the entries of the system matrices are either equal to the maxplusalgebraic zero element or to the maxplusalgebraic identity element. We give a lower bound for the minimal system order of a maxplusalgebraic boolean discrete event system. We show that the decision problem that corresponds to the boolean realization problem (i.e., deciding whether or not a boolean realization of a given order exists) ...
Computations of Uniform Recurrence Equations Using Minimal Memory Size
 SIAM J. Computing
, 1995
"... We consider a system of uniform recurrence equations (URE) of dimension one. We show how its computation can be carried out using minimal memory size with several synchronous processors. This result is then applied to register minimization for digital circuits and parallel computation of task gra ..."
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Cited by 6 (2 self)
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We consider a system of uniform recurrence equations (URE) of dimension one. We show how its computation can be carried out using minimal memory size with several synchronous processors. This result is then applied to register minimization for digital circuits and parallel computation of task graphs.
Minimal Realizations and State Space Transformations in the Symmetrized MaxAlgebra
, 1998
"... Similarity transformations between two different minimal realizations of a given impulse response of a Discrete Event System are discussed. In the symmetrized maxalgebra an explicit expression can be given for the transformation between an arbitrary minimal realization of a given impulse response a ..."
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Cited by 2 (0 self)
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Similarity transformations between two different minimal realizations of a given impulse response of a Discrete Event System are discussed. In the symmetrized maxalgebra an explicit expression can be given for the transformation between an arbitrary minimal realization of a given impulse response and a minimal realization of the same impulse response in a standard form. It is conjectured that a more general result holds which gives a transformation matrix between any two minimal realizations of an impulse response. We will illustrate the difficulties encountered when trying to prove this conjecture.
The set of realizations of a maxplus linear sequence is semipolyhedral
 JOURNAL OF COMPUTER AND SYSTEM SCIENCES
, 2011
"... ..."
Eigenproperties of the Information StateSpace
 Proc. IEEE Conf. on Systems, Man and Cybernetics
, 1995
"... The purpose of this paper is to examine the eigenproperties for a particular complex field mapping proposed in Bundell [2] to represent the 2dimensional TimeEvent Statespace proposed by Cohen et al [5]. This work extends the definition of the characteristic equation developed by Olsder & Roo ..."
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Cited by 1 (1 self)
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The purpose of this paper is to examine the eigenproperties for a particular complex field mapping proposed in Bundell [2] to represent the 2dimensional TimeEvent Statespace proposed by Cohen et al [5]. This work extends the definition of the characteristic equation developed by Olsder & Roos [7] for the Max algebra to the Information (TimeEvent) Statespace and examines an approach to its solution. An examples is given to illustrate the approach. 1. INTRODUCTION The specification and modelling of timing properties for realtime systems has become a major area of topical research. This heightened level of activity should benefit from the convergence of work by the realtime computation community and, more recently, the control engineering community. It is interesting to note the growing interest in this multidisciplinary area of endeavour [1] and the importance that may researchers attach to the crossfertilisation of ideas from one domain to another. This paper very much follow...
Partially supported by the European Grant BRAQMIPS of CEC DG XIII.
, 2004
"... We consider a system of uniform recurrence equations (URE) of dimension one. We show how its computation can be carried out using minimal memory size with several synchronous processors. This result is then applied to register minimization for digital circuits and parallel computation of task graphs ..."
Abstract
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We consider a system of uniform recurrence equations (URE) of dimension one. We show how its computation can be carried out using minimal memory size with several synchronous processors. This result is then applied to register minimization for digital circuits and parallel computation of task graphs.
On the Complexity of the Boolean Minimal Realization Problem in the MaxPlus Algebra
, 1998
"... One of the open problems in the maxplusalgebraic system theory for discrete event systems is the minimal realization problem. We consider a simplied version of the general minimal realization problem: the boolean minimal realization problem, i.e., we consider models in which the entries of the sys ..."
Abstract
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One of the open problems in the maxplusalgebraic system theory for discrete event systems is the minimal realization problem. We consider a simplied version of the general minimal realization problem: the boolean minimal realization problem, i.e., we consider models in which the entries of the system matrices are either equal to the maxplusalgebraic zero element or to the maxplus algebraic identity element. We show that the corresponding decision problem (i.e., deciding whether or not a boolean realization of a given order exists) is decidable, and that the boolean minimal realization problem can be solved in a number of elementary operations that is bounded from above by an exponential of the square of (any upper bound of) the minimal system order. INTRODUCTION The maxplusalgebra [1, 2], which has maximization and addition as its basic operations, is one of the frameworks that can be used to model a class of discrete event systems (DESs). Typical examples of DESs are exible...