On Application of Max-Plus Algebra to Synchronized Discrete Event System

Aminu, Abdulhadi; Olowo, S. E.; Sulaiman, I. M.; Bakar, N. Abu; Mamat, M.

doi:10.13189/ms.2021.090201

Cited by 3 publications

(2 citation statements)

References 12 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Now, by the same method as Example 4 we observe the det (𝑧 𝐴 ) and det (𝑧 𝐴 𝑖 ) where 𝐴 𝑖 = (𝑎 1 , … , 𝑎 𝑖−1 , 𝑏, 𝑎 𝑖+1 , … , 𝑎 𝑛 ) for 𝑖 ∈ {1,2,3}.𝑧 𝐴 = ( 𝑧 𝜀 ′ 𝑧 𝜀 ′ 𝑧 4 𝑧 1 𝑧 𝜀 ′ 𝑧 𝜀 ′ 𝑧 𝜀 ′ 𝑧 0 𝑧 𝜀 ′ ),then we get det(𝑧 𝐴 ) = 𝑧5 , 𝑑𝑜𝑚(𝐴) = 5 and 𝑠𝑖𝑔𝑛(𝐴) = +1. 𝑧 𝜀 ′ 𝑧4 𝑧 1 𝑧 𝜀 ′ 𝑧 𝜀 ′ 𝑧 0 𝑧 0 𝑧 𝜀 ′ ),then we get 𝑑𝑒𝑡(𝑧 𝐴 1 ) = 𝑧5 , 𝑑𝑜𝑚(𝐴 1 ) = 5 and 𝑠𝑖𝑔𝑛(𝐴1 ) = +1. 𝐴 2 = ( 𝜀′ 𝜀′ 4 1 1 𝜀′ 𝜀′ 0 𝜀′ ) , 𝑧 𝐴 2 = ( 𝑧 𝜀 ′ 𝑧 𝜀 ′ 𝑧 4 𝑧 1 𝑧 1 𝑧 𝜀 ′ 𝑧 0 𝑧 0 𝑧 𝜀 ′…”

mentioning

confidence: 85%

“…A system of linear equations 𝐴𝑥 = 𝑏 can be solved using Cramer's rule when 𝐴 is a non-singular matrix, or we can say det(A) ≠ 0 [1], [2]. Max-plus algebra is a set ℝ 𝑚𝑎𝑥 = {−∞} ∪ ℝ where ℝ is a set of real numbers, equipped with two binary operations ⊕ and ⊗ where 𝑥 ⊕ 𝑦 = 𝑚𝑎𝑥(𝑥, 𝑦) and 𝑥 ⊗ 𝑦 = 𝑥 + 𝑦 [3], [4]. The structure (ℝ 𝑚𝑎𝑥 ,⊕,⊗) is a semifield with a multiplication identity element 𝑒 = 0 and an addition identity element 𝜀 = −∞ [𝟓], [𝟔], [𝟕].…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Cramer’s Rule in Min-Plus Algebra

Putri,

Siswanto,

Kurniawan

2024

BAREKENG: J. Math. & App.

View full text Add to dashboard Cite

Cramer’s rule is one of a method for solving a system of linear equations in conventional algebra. The system of linear equation can be solved using Cramer’s rule if . Max-plus algebra is a set where is a set of real numbers, equipped with biner operations and where and . Min-plus Algebra is a set where is a set of real numbers, equipped with biner operations and where and . In max-plus algebra has been formulated Cramer’s rule to solve a system of linear equations. Because max-plus algebra is isomorphic to min-plus algebra, Cramer’s rule can be formulated into min-plus algebra. The purpose of this research is to determine the sufficient conditions for a system of linear equations can be solved using Cramer’s rule. The method used in this research is a literature study that reviews previous research related to min-plus algebra, max-plus algebra, and Cramer’s rule in max-plus algebra. By using the appropriate analogy in max-plus algebra, we can determine the sufficient conditions so that a system of linear equations in min-plus algebra can be solved using Cramer’s rule. Based on the research, the sufficient conditions for a system of linear equations can be solved using Cramer’s rule are for and with the Cramer’s rule is . For an invertible matrix A, Cramer’s rule can be written as .

show abstract

mentioning

confidence: 85%

Section: Introductionmentioning

confidence: 99%

Cramer’s Rule in Min-Plus Algebra

Putri,

Siswanto,

Kurniawan

2024

BAREKENG: J. Math. & App.

View full text Add to dashboard Cite

show abstract

An Algebraic Approach to the Solutions of the Open Shop Scheduling Problem

Cañadas,

Mendez,

Rojas

et al. 2023

2023 IEEE 13th International Conference on Pattern Recognition Systems (ICPRS)

View full text Add to dashboard Cite

An Algebraic Approach to the Solutions of the Open Shop Scheduling Problem

Cañadas,

Mendez,

Riaño-Rojas

et al. 2023

Computation

View full text Add to dashboard Cite

The open shop scheduling problem (OSSP) is one of the standard scheduling problems. It consists of scheduling jobs associated with a finite set of tasks developed by different machines. In this case, each machine processes at most one operation at a time, and the job processing order on the machines does not matter. The goal is to determine the completion times of the operations processed on the machines to minimize the largest job completion time, called Cmax. This paper proves that each OSSP has associated a path algebra called Brauer configuration algebra whose representation theory (particularly its dimension and the dimension of its center) can be given using the corresponding Cmax. value. It has also been proved that the dimension of the centers of Brauer configuration algebras associated with OSSPs with minimal Cmax. are congruent modulo the number of machines

show abstract

On Application of Max-Plus Algebra to Synchronized Discrete Event System

Cited by 3 publications

References 12 publications

Cramer’s Rule in Min-Plus Algebra

Cramer’s Rule in Min-Plus Algebra

An Algebraic Approach to the Solutions of the Open Shop Scheduling Problem

An Algebraic Approach to the Solutions of the Open Shop Scheduling Problem

Contact Info

Product

Resources

About