In addition, all the usual finite-state closure operations are supported: union, concatenation, Kleene star, and intersection.
There are really only three things that an FSA can do: concatenation (put two symbol sequences in sequence), union (choose between two different symbol sequences), or Kleene star (repeat some symbol sequence).
This is not a regular expression, since superscripts go beyond concatenation, union, and Kleene star. Such a language cannot be described with an FSA.
Axioms (1)-(11) say that the structure is an idempotent semiring under +, [center dot], 0, and 1, and the remaining axioms (12)-(17) say essentially that * behaves like the Kleene star
operator of formal language theory or the reflexive transitive closure operator of relational algebra.
Other topics discussed include tropical analysis of plurisubharmonic singularities, Kleene stars
and cyclic projectors in the geometry of Max cones, a tropical version of the Schauder fixed point theorem, and minimum representing measures in idempotent analysis.