Max-plus algebra

A max-plus algebra is a semiring over the union of real numbers and ${\displaystyle \varepsilon =-\infty }$, equipped with maximum and addition as the two binary operations. It can be used appropriately to determine marking times within a given Petri net and a vector filled with marking state at the beginning.

Let a and b be real scalars or ε. Then the operations maximum (implied by the max operator ${\displaystyle \oplus }$) and addition (plus operator ${\displaystyle \otimes }$) for these scalars are defined as

Watch: Max-operator ${\displaystyle \oplus }$ can easily be confused with the addition operation. Similar to the conventional algebra, all ${\displaystyle \otimes }$ - operations have a higher precedence than ${\displaystyle \oplus }$ - operations.

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