Table 1 Comparative ontology of complexity measures
From: Assembly theory and its relationship with computational complexity
Complexity Theory | Operands | Measures | Description/Details |
|---|---|---|---|
Algorithmic complexity | Classes of mathematical problems | Computational complexity Kolmogorov complexity; | Measures are concerned with optimal (minimal) descriptions of products of computational procedures, or the computational resources required for an algorithm that could produce the given output |
Compression and statistical complexity | Data and its representations | Huffman code; Lempel–Ziv–Welch compression; Information theory | Measures provide data transformations to generate reduced representations |
Physical complexity | States of physical systems | Logical depth; Thermodynamic depth; | Measures are concerned with the physical resource needed to compute a minimum description, or the probabilities of observed paths to produce a state |
Assembly theory | Physical objects | Assembly index | Measure is concerned with the minimum construction as an intrinsic and measurable physical attribute |
