Decomposing a k-valued Transducer into k Unambiguous Ones

We investigate the inner structure of finite-valued finite transducers. Our transducer models are the normalized finite transducer (NFT) and the non-deterministic generalized sequential machine (NGSM), which is a real-time NFT. We show: A k-valued NGSM M can be effectively decomposed into k unambiguous NGSMs M1,..., M k such that the transduction realized by M is the union of the transductions realized by M1..., M k . Each M i is of double exponential size and can be constructed in deterministic double exponential time. By reduction, this result can be extended to NFTs. As a consequence, the k-valued and the k-ambiguous NGSMs (NFTs) have the same generative power.

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