A New Quantitative Definition of the Complexity of Organized Matters

Table 2

Approach and machinery of the proposed definition and the existing ones.

Definitions	Approach	Rigorously specified	Machinery	Computa-bility	Key features
Kolmogorov complexity	Occam’s razor	✓	Turing machine		Descriptive
Effective complexity	Occam’s razor	✓	Turing machine		Descriptive
Logical depth	Occam’s razor	✓	Turing machine		Computational
Statistical complexity	Occam’s razor	✓	Stochastic finite-state automaton (hidden Markov; -machine)	✓	Distributional
Effective measure complexity	Information theoretical	✓	None	✓	Distributional
Natural complexity	Framework		None	—	—
Thermodynamics depth	Framework		None	—	—
Proposed definition	Occam’s razor	✓	Stochastic automaton form of circuit (oc-circuit)	✓	All (of the three)

—: Not easy to characterize.