极大加线性序列的实现集是半多面体的
The set of realizations of a max-plus linear sequence is semi-polyhedral
摘要：
我们表明，一个给定的尺寸的最大加线性序列的实现集是一个有限的多面体集，它可以计算从任何实现的序列。这产生了一个（昂贵的）算法来解决最大加最小实现问题。这些结果是来自一般的事实上的理性表达式幂等交换半环：我们更一般地表明，一个交换的理性表达式的系数在一个字母，产生一个给定的最大加线性序列的值的集合是一个半代数集的最大加意义。特别地，它是多面体集合的有限并集。
英文摘要：
We show that the set of realizations of a given dimension of a max-plus linear sequence is a finite union of polyhedral sets, which can be computed from any realization of the sequence. This yields an (expensive) algorithm to solve the max-plus minimal realization problem. These results are derived from general facts on rational expressions over idempotent commutative semirings: we show more generally that the set of values of the coefficients of a commutative rational expression in one letter that yield a given max-plus linear sequence is a semi-algebraic set in the max-plus sense. In particular, it is a finite union of polyhedral sets.
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