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

Proof of `Functions that weighted automata can be pre-composed with are rational`

groundedproofs/Lax132576Proofs/Results.lean · lax-132576

What this proof establishes

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

A function with which every weighted automaton can be pre-composed is rational (Theorem B.3.6, ⇐), from the source's Transducers.rationaliffweightedprecompTransducers.rational_iff_weighted_precomp applied over the semiring of regular languages.

Attribution

Theorem B.3.6 of Transducers; Lean proof by Aristotle (PartB/WeightedRegular.leanPartB/WeightedRegular.lean).