Is this Finite-State Transducer Sequentiable?

Abstract

Sequentiality is a desirable property of finite state transducers: such transducers are optimal for time efficiency. Not all transducers are sequentiable. Sequentialization algorithms of finite state transducers do not recognize whether a transducer is sequentiable or not and simply do not ever halt when it is not. Choffrut proved that sequentiality of finite state transducers is decidable. Béal et al. have proposed squaring to decide sequentiality. We propose a different procedure, which, with ε-closure extension, is able to handle letter transducers with arbitrary ε-ambiguities, too. Our algorithm is more economical than squaring, in terms of size. In different cases of non-sequentiability necessary and sufficient conditions of the ambiguity class of the transducer can be observed. These ambiguities can be mapped bijectively to particular basic patterns in the structure of the transducer. These patterns can be recognized, using finite state methods, in any transducer.