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We investigate the tree-to-tree functions computed by affine-transducers: tree automata whose memory consists of an affine -term instead of a finite state. They can be seen as variations on Gallot, Lemay and Salvati's Linear High-Order Deterministic Tree Transducers. When the memory is almost purely affine (\`a la Kanazawa), we show that these machines can be translated to tree-walking transducers (and with a purely affine memory, we get a reversible tree-walking transducer). This leads to a proof of an inexpressivity conjecture of on implicit automata in an affine -calculus. The key technical tool in our proofs is the Interaction Abstract Machine (IAM), an operational avatar of the geometry of interaction semantics of linear logic. We work with ad-hoc specializations to (almost) affine -terms of a tree-generating version of the IAM.
Nguyên et al. (Thu,) studied this question.