From Two-Way to One-Way Finite State Transducers

Abstract : Any two-way finite state automaton is equivalent to some one-way finite state automaton. This well-known result, shown by Rabin and Scott and independently by Shepherdson, states that two-way finite state automata (even non-deterministic) characterize the class of regular languages. It is also known that this result does not extend to finite string transductions: (deterministic) two-way finite state transducers strictly extend the expressive power of (functional) one-way transducers. In particular deterministic two-way transducers capture exactly the class of MSO-transductions of finite strings. In this paper, we address the following definability problem: given a function defined by a two-way finite state transducer, is it definable by a one-way finite state transducer? By extending Rabin and Scott's proof to transductions, we show that this problem is decidable. Our procedure builds a one-way transducer, which is equivalent to the two-way transducer, whenever one exists.
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Emmanuel Filiot, Olivier Gauwin, Pierre-Alain Reynier, Frédéric Servais. From Two-Way to One-Way Finite State Transducers. 28th Annual ACM/IEEE Symposium on Logic in Computer Science, Jun 2013, New Orleans, United States. pp.468-477, ⟨10.1109/LICS.2013.53⟩. ⟨hal-00946161⟩

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