Tropical abstractions of max-plus linear systems

Muhammad Syifa’ul Mufid*, Dieky Adzkiya, Alessandro Abate

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contributionpeer-review

5 Citations (Scopus)


This paper describes the development of finite abstractions of Max-Plus-Linear (MPL) systems using tropical operations. The idea of tropical abstraction is inspired by the fact that an MPL system is a discrete-event model updating its state with operations in the tropical algebra. The abstract model is a finite-state transition system: we show that the abstract states can be generated by operations on the tropical algebra, and that the generation of transitions can be established by tropical multiplications of matrices. The complexity of the algorithms based on tropical algebra is discussed and their performance is tested on a numerical benchmark against an existing alternative abstraction approach.

Original languageEnglish
Title of host publicationFormal Modeling and Analysis of Timed Systems - 16th International Conference, FORMATS 2018, Proceedings
EditorsDavid N. Jansen, Pavithra Prabhakar
PublisherSpringer Verlag
Number of pages17
ISBN (Print)9783030001506
Publication statusPublished - 2018
Event16th International Conference on Formal Modeling and Analysis of Timed Systems, FORMATS 2018 - Beijing, China
Duration: 4 Sept 20186 Sept 2018

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume11022 LNCS
ISSN (Print)0302-9743
ISSN (Electronic)1611-3349


Conference16th International Conference on Formal Modeling and Analysis of Timed Systems, FORMATS 2018


  • Abstraction
  • Definite form
  • Difference-bound matrix
  • MPL system
  • Reachability
  • Tropical algebra


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