The max tropical semiring can be used appropriately to determine marking times within a given Petri net and a vector filled with marking state at the beginning: ${\displaystyle -\infty }$  (unit for max, tropical addition) means "never before", while 0 (unit for addition, tropical multiplication) is "no additional time".

Tropical cryptography is cryptography based on the tropical semiring.

Tropical geometry is an analog to algebraic geometry, using the tropical semiring.

• Butkovič, Peter (2010), Max-linear Systems: Theory and Algorithms, Springer Monographs in Mathematics, Springer-Verlag, doi:10.1007/978-1-84996-299-5, ISBN 978-1-84996-298-8
• Bernd Heidergott; Geert Jan Olsder; Jacob van der Woude (2005). Max Plus at Work: Modeling and Analysis of Synchronized Systems: A Course on Max-Plus Algebra and Its Applications. Princeton University Press. p. 224. ISBN 978-0-69111763-8.

• Lunar arithmetic

• MaxPlus algebra
• Max Plus working group, INRIA Rocquencourt