Computation of the Transient in Max-Plus Linear Systems via SMT-Solving

Abate, Alessandro; Cimatti, Alessandro; Micheli, Andrea; Mufid, Muhammad Syifa'ul

doi:10.1007/978-3-030-57628-8_10

Cited by 7 publications

(3 citation statements)

References 27 publications

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“…Furthermore, Propositions 3 and 4 indicate the equivalent relation between periodic behavior and lasso orbits. Proposition 2 ( [52]). Suppose we have a regular matrix A ∈ R n×n max with a maximum eigenvalue λ and cycle-time vector χ.…”

Section: Transient and Cyclicitymentioning

confidence: 99%

Bounded Model Checking of Max-Plus Linear Systems via Predicate Abstractions

Mufid

Adzkiya

Abate

2019

Lecture Notes in Computer Science

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This paper introduces the abstraction of max-plus linear (MPL) systems via predicates. Predicates are automatically selected from system matrix, as well as from the specifications under consideration. We focus on verifying time-difference specifications, which encompass the relation between successive events in MPL systems. We implement a bounded model checking (BMC) procedure over a predicate abstraction of the given MPL system, to verify the satisfaction of time-difference specifications. Our predicate abstractions are experimentally shown to improve on existing MPL abstractions algorithms. Furthermore, with focus on the BMC algorithm, we can provide an explicit upper bound on the completeness threshold by means of the transient and the cyclicity of the underlying MPL system.

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Section: Transient and Cyclicitymentioning

confidence: 99%

Bounded Model Checking of Max-Plus Linear Systems via Predicate Abstractions

Mufid

Adzkiya

Abate

2019

Lecture Notes in Computer Science

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“…The basic understanding and operation of max-plus algebra and matrix operations for max-plus algebra that used in this article refers to [9]- [11]. This article also describes the eigenvalues and eigenvectors in max-plus algebra referring to [3], [4], [12], [13]. Next, to determine the eigenvalues and eigenvectors of the matrix of max-plus algebra, an algorithm is taken from the article [5], [14].…”

Section: Introductionmentioning

confidence: 99%

Application of System Max-Plus Linear Equations on Serial Manufacturing Machine With Storage Unit

Maharani¹,

Suparwanto

2022

BAREKENG: J. Il. Mat. & Ter.

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The set together with the operation maximum (max) denoted as and addition (+) denoted as is called max-plus algebra. Max-plus algebra may be used to apply algebraically a few programs of Discrete Event Systems (DES), certainly one of the examples in the production system. In this study, the application of max-plus algebra in a serial manufacturing machine with a storage unit is discussed. The results of this are the generalization system max-plus-linear equations on a production system that is, in addition, noted the max-plus-linear time-invariant system. From the max-plus-linear time-invariant system, it can be obtained the equation which is then used to determine the beginning time of a production system so the manufacturing machine work periodically. The eigenvector and eigenvalue of the matrix are then used to find the beginning time and the period time of the manufacturing machine. Furthermore, the time when the product leaves the manufacturing machine with the time while the raw material enters the manufacturing machine is given and vice versa are obtained from the max-plus-linear time-invariant system that is can be formed in the equation .

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“…The question seems to be related to the topic of transience bounds in max-plus linear systems (see, e.g.,[26,27]). …”

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confidence: 99%