Squaring transducers: an efficient procedure for deciding functionality and sequentiality

Béal, Marie–Pierre; Carton, Olivier; Prieur, Christophe; Sakarovitch, Jacques

doi:10.1016/s0304-3975(01)00214-6

Cited by 69 publications

(76 citation statements)

References 8 publications

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“…Hence, it suffices to decide whether T defines a function (i.e. is functional), which can be done in PTIME in the size of T (see for instance [2]). It remains to show how to construct T .…”

Section: Proof (Of Proposition 5)mentioning

confidence: 99%

Decidable Weighted Expressions with Presburger Combinators

Filiot

Mazzocchi

Raskin

2017

Fundamentals of Computation Theory

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Abstract. In this paper, we investigate the expressive power and the algorithmic properties of weighted expressions, which define functions from finite words to integers. First, we consider a slight extension of an expression formalism, introduced by Chatterjee. et. al. in the context of infinite words, by which to combine values given by unambiguous (max, +)-automata, using Presburger arithmetic. We show that important decision problems such as emptiness, universality and comparison are PSPACE-C for these expressions. We then investigate the extension of these expressions with Kleene star. This allows to iterate an expression over smaller fragments of the input word, and to combine the results by taking their iterated sum. The decision problems turn out to be undecidable, but we introduce the decidable and still expressive class of synchronised expressions.

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“…Hence, it suffices to decide whether T defines a function (i.e. is functional), which can be done in PTIME in the size of T (see for instance [2]). It remains to show how to construct T .…”

Section: Proof (Of Proposition 5)mentioning

confidence: 99%

Decidable Weighted Expressions with Presburger Combinators

Filiot

Mazzocchi

Raskin

2017

Fundamentals of Computation Theory

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“…A transducer t is called functional if |t(w)| ≤ 1, for every word w. Transducer functionality can be tested in polynomial time [2]. A triple of words (w, z, z ) is called a witness of t's nonfunctionality, if z = z and z, z ∈ t(w).…”

Section: Examplementioning

confidence: 99%

Implementation of Code Properties via Transducers

Konstantinidis¹,

Meijer²,

Moreira

et al. 2016

Implementation and Application of Automata

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Abstract. The FAdo system is a symbolic manipulator of formal language objects, implemented in Python. In this work, we extend its capabilities by implementing methods to manipulate transducers and we go one level higher than existing formal language systems and implement methods to manipulate objects representing classes of independent languages (widely known as code properties). Our methods allow users to define their own code properties and combine them between themselves or with fixed properties such as prefix codes, suffix codes, error detecting codes, etc. The satisfaction and maximality decision questions are solvable for any of the definable properties. The new online system LaSer allows one to query about a code property and obtain the answer in a batch mode. Our work is founded on independence theory as well as the theory of rational relations and transducers, and contributes with improved algorithms on these objects.

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“…13 The notion of twins property was originally introduced for unweighted finitestate transducers by [15,16] and was shown to be decidable. Polynomial-time algorithms were later given to test this property for functional transducers in time O(|Q| 4 (|Q| 2 + |E| 2 )|∆|) by [58], O(|Q| 4 (|Q| 2 + |E| 2 )) by [11], and O(|Q| 2 (|Q| 2 + |E| 2 )) by [3], where Q is the set of states of the input transducer, E the set of its transitions and ∆ the output alphabet. 14 An automaton is cycle-unambiguous if for any state q and any string x there exists at most one cycle at q labeled with x.…”

Section: Theorem 5 ([38]mentioning

confidence: 99%

Weighted Automata Algorithms

Mohri

2009

Monographs in Theoretical Computer Science. An EATCS Series

146

149

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This chapter presents several fundamental algorithms for weighted automata and transducers. While the mathematical counterparts of weighted transducers, rational power series, have been extensively studied in the past [22,54,13,36], several essential weighted transducer algorithms, e.g., composition, determinization, minimization, have been devised only in the last decade [38,43], in part motivated by novel applications in speech recognition, speech synthesis, machine translation, other areas of natural language processing, image processing, optical character recognition, and more recently machine learning.These algorithms can be viewed as the generalization to the weighted transducer case of the standard algorithms for unweighted acceptors. However, this generalization is often not straightforward and has required a number of specific studies either because the old schema could not be applied in the presence of weights and a novel technique was required, as in the case of composition [50,46], or because of the analysis of the conditions of application of an algorithm as in the case of determinization [38,3].The chapter favors a presentation of weighted automata and transducers in terms of graphs, the natural concepts for an algorithmic description and complexity analysis. Also, while power series lead to more concise and rigorous proofs in most cases [36], proofs related to questions of ambiguity naturally require the introduction of paths and reasoning on graph concepts. PreliminariesThis section introduces the definitions and notation related to weighted finitestate transducers, weighted transducers for short, and weighted automata.

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Squaring transducers: an efficient procedure for deciding functionality and sequentiality

Cited by 69 publications

References 8 publications

Decidable Weighted Expressions with Presburger Combinators

Decidable Weighted Expressions with Presburger Combinators

Implementation of Code Properties via Transducers

Weighted Automata Algorithms

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