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MSO definable string transductions and two-way finite state transducers

Joost Engelfriet·Hendrik Jan Hoogeboom
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Abstract

String transductions that are definable in monadic second-order (mso) logic (without the use of parameters) are exactly those realized by deterministic two-way finite state transducers. Nondeterministic mso definable string transductions (i.e., those definable with the use of parameters) correspond to compositions of two nondeterministic two-way finite state transducers that have the finite visit property. Both families of mso definable string transductions are characterized in terms of Hennie machines, i.e., two-way finite state transducers with the finite visit property that are allowed to rewrite their input tape.

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Joost Engelfriet, Hendrik Jan Hoogeboom. 1999-06-04. MSO definable string transductions and two-way finite state transducers. https://arxiv.org/abs/cs/9906007

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