One-way definability of two-way word transducers

Baschenis, Félix; Gauwin, Olivier; Muscholl, Anca; Puppis, Gabriele

doi:10.23638/lmcs-14(4:22)2018

Cited by 2 publications

(1 citation statement)

References 24 publications

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“…For such kind of monoids, Theorem 1 performs considerably better than previously known methods to find idempotent factors. For instance, it was used in [14] to close the complexity gap left in [1] for the problem of deciding whether the function defined by a given two-way word transducer is definable by a one-way transducer.…”

Section: Computing the Regular D-lengthmentioning

confidence: 99%

A Ramsey Theorem for Finite Monoids

Jecker

2021

Preprint

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Repeated idempotent elements are commonly used to characterise iterable behaviours in abstract models of computation. Therefore, given a monoid M , it is natural to ask how long a sequence of elements of M needs to be to ensure the presence of consecutive idempotent factors. This question is formalised through the notion of the Ramsey function RM of a finite monoid M , obtained by mapping every k ∈ N to the minimal integer RM (k) such that every word u ∈ M * of length RM (k) contains k consecutive non-empty factors that correspond to the same idempotent element of M .In this work, we study the behaviour of the Ramsey function RM by investigating the regular D-length of M , defined as the largest size L(M ) of a submonoid of M isomorphic to the set of natural numbers {1, 2, . . . , L(M )} equipped with the max operation. We show that the regular D-length of M determines the degree of RM , by proving that kTo allow applications of this result, we provide the value of the regular D-length of diverse monoids. In particular, we prove that the full monoid of n × n Boolean matrices, which is used to express transition monoids of non-deterministic automata, has a regular D-length of n 2 +n+2 2 .

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Section: Computing the Regular D-lengthmentioning

confidence: 99%

A Ramsey Theorem for Finite Monoids

Jecker

2021

Preprint

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One-way Resynchronizability of Word Transducers

Bose

Krishna

Muscholl

et al. 2021

Preprint

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The origin semantics for transducers was proposed in 2014, and it led to various characterizations and decidability results that are in contrast with the classical semantics. In this paper we add a further decidability result for characterizing transducers that are close to oneway transducers in the origin semantics. We show that it is decidable whether a non-deterministic two-way word transducer can be resynchronized by a bounded, regular resynchronizer into an origin-equivalent oneway transducer. The result is in contrast with the usual semantics, where it is undecidable to know if a non-deterministic two-way transducer is equivalent to some one-way transducer.

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One-way definability of two-way word transducers

Cited by 2 publications

References 24 publications

A Ramsey Theorem for Finite Monoids

A Ramsey Theorem for Finite Monoids

One-way Resynchronizability of Word Transducers

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