On weakly ambiguous finite transducers

Authors:
Nicolae Santean;Sheng Yu
Affiliations:
Department of Computer Science, University of Western Ontario, London, ON, Canada;Department of Computer Science, University of Western Ontario, London, ON, Canada
Venue:
DLT'06 Proceedings of the 10th international conference on Developments in Language Theory
Year:
2006

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Abstract

By weakly ambiguous (finite) transducers we mean those transducers that, although being ambiguous, may be viewed to be at arm's length from unambiguity. We define input-unambiguous (IU) and input-deterministic (ID) transducers, and transducers with finite codomain (FC). IU transductions are characterized by nondeterministic bimachines and ID transductions can be represented as a composition of sequential functions and finite substitutions. FC transductions are recognizable and can be expressed as finite unions of subsequential functions. We place these families along with uniformly ambiguous (UA) and finitely ambiguous (FA) transductions in a hierarchy of ambiguity. Finally, we show that restricted nondeterministic bimachines characterize FA transductions. Perhaps the most important aspect of this work consists in defining nondeterministic bimachines and describing their power by linking them with weakly ambiguous finite transducers (IU and FA).