pyphi.automorphism

Behavior-aware substrate canonicalization.

A substrate’s identity is its connectivity, its per-node TPM, and its per-node alphabet sizes. A node permutation is a substrate automorphism only when it preserves all three – so a node implementing one mechanism is never identified with a node implementing a different one, even when their wiring is identical.

Canonicalization is exact: the automorphism group and canonical form are found by enumerating node permutations, which is factorial in the number of nodes.

Functions

are_structures_isomorphic(ces1, ces2)	Whether two cause-effect structures are equal up to a bijection of their node indices, at the resolution of structure_signature().
are_substrates_isomorphic(s1, s2)	Whether some node permutation maps s1's connectivity, TPM, and alphabet sizes onto s2's.
canonical_state(substrate, state)	Map state into canonical coordinates, reduced over the automorphism orbit.
structure_signature(ces[, mapping])	A canonical, order-independent value key for a cause-effect structure under a node-index mapping.
substrate_automorphisms(substrate)	All node permutations preserving connectivity, TPM, and alphabet sizes.
substrate_canonical_form(substrate)	Return (canonical_substrate, canonical_permutation).