Graphs and algorithms
Asymptotic expansions for dynamic programming recursions with general nonnegative matrices
Journal of Optimization Theory and Applications
Alternative proof of Sine's theorem on the size of a regular polygon in Rn with the ℓ∞ -metric
Discrete & Computational Geometry
Monotone structure in discrete-event systems
Monotone structure in discrete-event systems
ICCAD '92 Proceedings of the 1992 IEEE/ACM international conference on Computer-aided design
Scheduling Parallel Computations
Journal of the ACM (JACM)
Stochastic Optimal Control: The Discrete-Time Case
Stochastic Optimal Control: The Discrete-Time Case
Some Ergodic Results on Stochastic Iterative Discrete Events Systems
Discrete Event Dynamic Systems
An Algorithm for Exact Bounds on the Time Separation of Events in Concurrent Systems
IEEE Transactions on Computers
IEEE Transactions on Parallel and Distributed Systems
Dynamic Matrices and the Cost Analysis of Concurrent Programs
AMAST '95 Proceedings of the 4th International Conference on Algebraic Methodology and Software Technology
Spectral theorem for convex monotone homogeneous maps, and ergodic control
Nonlinear Analysis: Theory, Methods & Applications
Asymptotic Properties of Monotonic Nonexpansive Mappings
Discrete Event Dynamic Systems
The many benefits of putting stack filters into disjunctive or conjunctive normal form
Discrete Applied Mathematics - Special issue: Boolean and pseudo-boolean funtions
Max-plus Algebraic Tools for Discrete Event Systems, Static Analysis, and Zero-Sum Games
FORMATS '09 Proceedings of the 7th International Conference on Formal Modeling and Analysis of Timed Systems
The many benefits of putting stack filters into disjunctive or conjunctive normal form
Discrete Applied Mathematics - Special issue: Boolean and pseudo-boolean funtions
A survey of the theory of min-max systems
ICIC'05 Proceedings of the 2005 international conference on Advances in Intelligent Computing - Volume Part II
A policy iteration algorithm for computing fixed points in static analysis of programs
CAV'05 Proceedings of the 17th international conference on Computer Aided Verification
RelMiCS'06/AKA'06 Proceedings of the 9th international conference on Relational Methods in Computer Science, and 4th international conference on Applications of Kleene Algebra
Playing games with scenario- and resource-aware SDF graphs through policy iteration
DATE '12 Proceedings of the Conference on Design, Automation and Test in Europe
| Hi-index | 5.23 |
Discrete event systems provide a useful abstraction for modelling a wide variety of systems: digital circuits, communication networks, manufacturing plants, etc. Their dynamics--stability, equilibrium states, cyclical behaviour, asymptotic average delays--are of vital importance to system designers. However, in marked contrast to continuous dynamical systems, there has been little systematic mathematical theory that designers can draw upon. In this paper, we survey the development of such a theory, based on the dynamics of maps which are nonexpansive in the l∞ norm. This has its origins in linear algebra over the max-plus semiring but extends to a nonlinear theory that encompasses a variety of problems arising in other mathematical disciplines. We concentrate on the mathematical aspects and set out several open problems.