Draft — mutable and not usable as a dependency; its citation marks the draft state.

Proof of `Aperiodic Mealy machines are compositions of flip-flops`

groundedproofs/Lax765601Proofs/Results.lean · lax-765601

What this proof establishes

no assumptions

Assuming the claims on the left, the claim on the right holds — checked by the archive's pipeline. Proof code is not displayed here.

Read the Lean proof on GitHub

Description

An aperiodic Mealy function is a composition of flip-flops (the hard half of Theorem A.2.8): by Lemma A.2.11 some machine computing it satisfies the stabilisation condition (*), and the Krohn–Rhodes construction run for that machine only produces flip-flops (Transducers.krohnrhodesflipFlopTransducers.krohn_rhodes_flipFlop, from RequestProject/PartA/StateTransAperiodic.leanRequestProject/PartA/StateTransAperiodic.lean).

Attribution

Theorem A.2.8 of Transducers, left-to-right; Lean proof by Aristotle (Transducers.aperiodiciffflipflopcompositionTransducers.aperiodic_iff_flipflop_composition).