Max-plus algebra
نویسندگان
چکیده
The max-plus semiring Rmax is the set R∪{−∞}, equipped with the addition (a, b) 7→ max(a, b) and the multiplication (a, b) 7→ a + b. The identity element for the addition, zero, is −∞, and the identity element for the multiplication, unit, is 0. To illuminate the linear algebraic nature of the results, the generic notations +, , × (or concatenation), 0 and 1 are used for the addition, the sum, the multiplication, the zero and the unit of Rmax respectively, so that when a, b belong to Rmax, a+ b will mean max(a, b), a× b or ab will mean the usual sum a + b. We use blackboard (double struck) fonts to denote the max-plus operations (compare “+” with “+”).
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