From max-plus algebra to nonexpansive mappings: A nonlinear theory for discrete event systems.

DOI10.1016/S0304-3975(02)00235-9zbMath1036.93045MaRDI QIDQ1870590

Jeremy Gunawardena

Publication date: 14 May 2003

Published in: Theoretical Computer Science (Search for Journal in Brave)

zbMATH Keywords

Fixed pointMax-plus semiringCycle timeNonnegative matrixDiscrete event systemNonexpansive mapNonlinear eigenvalueTopical function

Mathematics Subject Classification ID

Discrete event control/observation systems (93C65) Applications of operator theory in systems, signals, circuits, and control theory (47N70) Nonlinear operators and their properties (47H99)

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Cites Work

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• Extension of uniformly continuous transformations and hyperconvex metric spaces
• Asymptotic expansions for dynamic programming recursions with general nonnegative matrices
• Asymptotic behavior of nonexpansive mappings in normed linear spaces
• Omega limit sets of nonexpansive maps: Finiteness and cardinality estimates
• Eigenvalues of dynamic max-min systems
• Alternative proof of Sine's theorem on the size of a regular polygon in \(\mathbb{R}{}^ n\) with the \(\ell{}_ \infty\)-metric
• Minimax algebra
• Min-max functions
• Some ergodic results on stochastic iterative discrete events systems
• The cycle time vector of D-A-D functions
• Dioïds and semirings: Links to fuzzy sets and other applications
• The spectrum of a nonlinear operator associated with a matrix
• A linear-system-theoretic view of discrete-event processes and its use for performance evaluation in manufacturing
• A Nonlinear Perron-Frobenius Theorem
• Hilbert’s projective metric and iterated nonlinear maps
• Iterated nonlinear maps and Hilbert’s projective metric. II
• Invariant Half-Lines of Nonexpansive Piecewise-Linear Transformations
• Performance Evaluation of Asynchronous Concurrent Systems Using Petri Nets
• Some Relations Between Nonexpansive and Order Preserving Mappings
• Growth Optimality for Branching Markov Decision Chains
• The Asymptotic Theory of Stochastic Games
• On Stochastic Games with Stationary Optimal Strategies
• The duality theorem for min-max functions
• Existence and uniqueness of diffusions on finitely ramified self-similar fractals
• An algorithm for exact bounds on the time separation of events in concurrent systems
• The Perron-Frobenius theorem for homogeneous, monotone functions
• Unison, canon, and sluggish clocks in networks controlled by a synchronizer
• A constructive fixed point theorem for min-max functions
• Scheduling Parallel Computations
• An Algebra for Network Routing Problems

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