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Understanding the Theory of Karp, Miller and Winograd

Journal of Applied Mathematics and Physics 2024年第4期12卷 1203-1236页

作者： Athanasios I. Margaris Department of Digital Systems Gaiopolis Campus University of Thessaly Larissa Greece

The objective of this tutorial is to present the fundamental theory of Karp, Miller and Winograd, whose seminal paper laid the foundations regarding the systematic description of the organization of computations in systems of uniform recurrent equations by means of graph structures, via the definition of computability conditions and techniques for the construction of one-dimensional and multi-dimensional scheduling functions. Besides the description of this theory, the paper presents improvements and revisions made by other authors and furthermore, points out the differences regarding the conditions of causality and dependency between the general case of systems of recurrent equations and the special case of multiple nested loops.

关键词： Computability Scheduling Computations recurrent equations

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A Generalized Eigenmode Algorithm for Reducible Regular Matrices over the Max-Plus Algebra

A Generalized Eigenmode Algorithm for Reducible Regular Matr...

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2009中国控制与决策会议

作者： Zvi Retchkiman Knigsberg Instituto Politécnico Nacional CIC Mineria 17-2Col.EscandonMexico D.F 11800Mexico

＜正＞In this paper an algorithm for computing a generalized eigenmode of reducible regular matrices over the max-plus algebra is *** a matrix of finite size,the problem consists in giving an algorithm which will tell us how to compute its generalized eigenmode over the max plus algebra. The solution to the problem is achieved by studying some type of recurrent *** fact, by transforming the reducible regular matrix into its normal form,and considering a very specific recurrent equation,an explicit mathematical characterization is obtained,upon which the algorithm is constructed.

关键词： Index terms- Max-Plus Algebra Reducible Matrices Eigenmode recurrent equations Algorithm.

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Timetable Design for a Helicopter Maintenance Process using Timed Event Petri Nets and Max-Plus Algebra

Timetable Design for a Helicopter Maintenance Process using ...

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2010 Chinese Control and Decision Conference

作者： Zvi Retchkiman Knigsberg Instituto Politecnico Nacional CIC Mineria 17-2Col.EscandonMexico D.F 11800Mexico

＜正＞In this paper an algorithm for computing a generalized eigenmode of reducible regular matrices over the max-plus algebra is applied to a helicopter maintenance process.A timed event Petri net model is constructed from the state transition dynamics table that characterizes the transport system.A max-plus recurrence equation,with a reducible and regular matrix,is associated to the timed event Petri ***,given the reducible and regular matrix,the problem consists in giving an algorithm which will tell us how to compute its generalized eigenmode over the max plus algebra. The solution to the problem is achieved by studying some type of recurrence *** fact,by transforming the reducible regular matrix into its normal form,and considering a very specific recurrence equation, an explicit mathematical characterization is obtained, upon which the algorithm is *** generalized eigenmode obtained sets a timetable for the helicopter maintenance process.

关键词： Max-Plus Algebra Reducible Matrices Eigenmode recurrent equations Algorithm Helicopter Maintenance Process

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