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Register a new userEquivalence of Linear Tree Transducers with Output in the Free Group
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Added by
Raphaela L\\\"obel
Publication date
2020
fields
Informatics Engineering
and research's language is
English
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No Arabic abstract
We show that equivalence of deterministic linear tree transducers can be decided in polynomial time when their outputs are interpreted over the free group. Due to the cancellation properties offered by the free group, the required constructions are not only more general, but also simpler than the corresponding constructions for proving equivalence of deterministic linear tree-to-word transducers.
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A language over an alphabet $B = A cup overline{A}$ of opening ($A$) and closing ($overline{A}$) brackets, is balanced if it is a subset of the Dyck language $D_B$ over $B$, and it is well-formed if all words are prefixes of words in $D_B$. We show that well-formedness of a context-free language is decidable in polynomial time, and that the longest common reduced suffix can be computed in polynomial time. With this at a hand we decide for the class 2-TWs of non-linear tree transducers with output alphabet $B^*$ whether or not the output language is balanced.
We consider input-deterministic finite state transducers with infinite inputs and infinite outputs, and we consider the property of Borel normality on infinite words. When these transducers are given by a strongly connected set of states, and when the input is a Borel normal sequence, the output is an infinite word such that every word has a frequency given by a weighted automaton over the rationals. We prove that there is an algorithm that decides in cubic time whether an input-deterministic transducer preserves normality.
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Deterministic two-way transducers on finite words have been shown by Engelfriet and Hoogeboom to have the same expressive power as MSO-transductions. We introduce a notion of aperiodicity for these transducers and we show that aperiodic transducers correspond exactly to FO-transductions. This lifts to transducers the classical equivalence for languages between FO-definability, recognition by aperiodic monoids and acceptance by counter-free automata.
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