Information-based complexity (IBC) is a well-defined complexity measure of any object given a description in a language and a classifier that identifies those descriptions with the object. Of course, the exact numerical value will vary according to the descriptive language and classifier, but under certain universality conditions (eg the classifier identifies programs of a universal Turning machine that halt and output the same value), asymptotically, the complexity measure is independent of the classifier up to a constant of O(1). The hypothesis being investigated in this work that any practical IBC measure will similarly be asymptotically equivalent to any other practical IBC measure. Standish presented an IBC measure for graphs ${\cal C}$ that encoded graphs by their links, and identifies graphs as those that are automorphic to each other. An interesting alternate graph measure is {\em star complexity}, which is defined as the number of union and intersection operations of basic stars that can generate the original graph. Whilst not an IBC itself, it can be related to an IBC (called ${\cal C}^*$) that is strongly correlated with star complexity. In this paper, 10 and 22 vertex graphs are constructed up to a star complexity of 8, and the ${\cal C}^*$ compared emprically with ${\cal C}$. Finally, an easily computable upper bound of star complexity is found to be strongly related to ${\cal C}$.

翻译：信息基础复杂度（IBC）是一种明确定义的复杂度度量，适用于任何给定语言描述及能够识别该描述与对象对应关系的分类器所定义的对象。当然，其具体数值会因描述语言和分类器的不同而变化，但在某些普适性条件下（例如分类器识别出通用图灵机中停机并输出相同值的程序），该复杂度度量在渐近意义上独立于分类器，仅存在O(1)级别的常数差异。本研究探讨的假设是：任何实用的IBC度量在渐近意义上都将与其他实用的IBC度量等价。Standish提出了一种针对图的IBC度量${\cal C}$，该方法通过图的边链接对图进行编码，并将自同构的图视为同一图。一个有趣的替代性图度量是{\em 星复杂度}，其定义为通过基本星的并集与交集运算能够生成原图所需的最小操作次数。虽然星复杂度本身并非IBC度量，但可将其关联于一种与星复杂度强相关的IBC度量（称为${\cal C}^*$）。本文构建了顶点数为10和22、星复杂度不超过8的图，并通过实证方法比较了${\cal C}^*$与${\cal C}$的度量结果。最后，研究发现星复杂度的一个易于计算的上界与${\cal C}$存在强关联性。