Abstract

This paper deals with the notion of subsequential transducer, i. e., of finite deterministic automaton whose transitions are provided with an "output". Its purpose is twofold. First it is meant to give better access to the result saying, in loose terms, that it is possible to define a notion of morphism on subsequential transducers in such a way that the ordinary theory of deterministic automata carries over to subsequential transducers. In particular, given a function realized by some subsequential transducer, there exists a "minimal" subsequential transducer realizing it such that all trimmed subsequential transducers map onto it. This is a critical departure from the more general case of rational functions where the existence of such a minimal object is still unsettled, cf. [13]. Thus, though more complex than finite deterministic automata, subsequential transducers enjoy the same "syntactical" property and the techniques for proving this fact are not substantially different. This appeared in my doctorial thesis and in the proceedings of the ICALP'79 conference. To be more precise, this was actually stated in a slightly larger context, since the function was supposed to map the free monoid into the free group. In spite of being more general and easily "downgradable" to free monoids, this formalism has probably confused some readers and obscured the fact that it was dealing with free monoids also.

Citations