Transducers, logic and algebra for functions of finite words

Filiot, Emmanuel; Reynier, Pierre-Alain

doi:10.1145/2984450.2984453

Cited by 36 publications

(51 citation statements)

References 29 publications

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“…To better understand the role of iteration, the technical focus of the paper is on the firstorder fragment of regular string-to-string functions [15,Section 4.3]. Our main technical result, Theorem 13, shows a family of atomic functions and combinators that describes exactly the first-order fragment.…”

Section: Introductionmentioning

confidence: 99%

Regular and First-Order List Functions

Bojańczyk

Daviaud

Krishna

2018

Proceedings of the 33rd Annual ACM/IEEE Symposium on Logic in Computer Science

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We define two classes of functions, called regular (respectively, first-order) list functions, which manipulate objects such as lists, lists of lists, pairs of lists, lists of pairs of lists, etc. The definition is in the style of regular expressions: the functions are constructed by starting with some basic functions (e.g. projections from pairs, or head and tail operations on lists) and putting them together using four combinators (most importantly, composition of functions). Our main results are that first-order list functions are exactly the same as first-order transductions, under a suitable encoding of the inputs; and the regular list functions are exactly the same as mso-transductions.

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Section: Introductionmentioning

confidence: 99%

Regular and First-Order List Functions

Bojańczyk

Daviaud

Krishna

2018

Proceedings of the 33rd Annual ACM/IEEE Symposium on Logic in Computer Science

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“…of functions computed by automata with output. As of the time of writing, it seems likely that in EAλ , Str ⊸ Str captures the well-known class of regular functions (see [8] for an overview of classical transduction classes, including regular functions), and that the class defined by !Str ⊸ !Str also admits an automata-theoretic characterization.…”

Section: Resultsmentioning

confidence: 99%

On the Elementary Affine Lambda-Calculus with and Without Fixed Points

Nguyên

2019

Electron. Proc. Theor. Comput. Sci.

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The elementary affine λ -calculus was introduced as a polyvalent setting for implicit computational complexity, allowing for characterizations of polynomial time and hyperexponential time predicates. But these results rely on type fixpoints (a.k.a. recursive types), and it was unknown whether this feature of the type system was really necessary. We give a positive answer by showing that without type fixpoints, we get a characterization of regular languages instead of polynomial time. The proof uses the semantic evaluation method. We also propose an aesthetic improvement on the characterization of the function classes FP and k-FEXPTIME in the presence of recursive types. * Partially supported by the ANR project ELICA (ANR-14-CE25-0005).On the elementary affine λ -calculus with and without type fixpoints Type fixpoints and Scott encodings We wish to draw attention to a particular feature of this language: the presence of type fixpoints 1 , a.k.a. recursive types. An example is the type of Scott binary strings:In the elementary affine λ -calculus as defined in [2], this recursive equation can be turned into a valid type definition, by using a fixed point operator µ on types (this explains our name µEAλ ):

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“…This finite-state technology not only describes reduplication as a process which applies to infinitely many words of unbounded size, but it does so without the state-space explosion. The type of transducer which accomplishes this is known as a 2-way Finite-State Transducer or 2-way FST (Savitch, 1982;Engelfriet and Hoogeboom, 2001;Filiot and Reynier, 2016). While these computer scientists are well aware that 2-way FSTS can model unbounded copying, this is the first use of 2-way FSTs within computational linguisticst to our knowledge.…”

Section: ) Wanita→wanita∼wanitamentioning

confidence: 99%

“…It only ever advances as strings are written. Below is a formalization of 2-way FSTs based on Filiot and Reynier (2016) and Shallit (2008). We adopt the convention that inputs to a 2-way FST are flanked with the start ( ) and end boundaries ( ).…”

Section: Definitionmentioning

confidence: 99%

Modeling Reduplication with 2-way Finite-State Transducers

Dolatian¹,

Heinz²

2018

Proceedings of the Fifteenth Workshop on Computational Research in Phonetics, Phonology, and Morphology

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This article describes a novel approach to the computational modeling of reduplication. Reduplication is a well-studied linguistic phenomenon. However, it is often treated as a stumbling block within finite-state treatments of morphology. Most finite-state implementations of computational morphology cannot adequately capture the productivity of unbounded copying in reduplication, nor can they adequately capture bounded copying. We show that an understudied type of finite-state machines, two-way finite-state transducers (2way FSTs), captures virtually all reduplicative processes, including total reduplication. 2-way FSTs can model reduplicative typology in a way which is convenient, easy to design and debug in practice, and linguisticallymotivated. By virtue of being finite-state, 2way FSTs are likewise incorporable into existing finite-state systems and programs. A small but representative typology of reduplicative processes is described in this article, alongside their corresponding 2-way FST models.

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Transducers, logic and algebra for functions of finite words

Cited by 36 publications

References 29 publications

Regular and First-Order List Functions

Regular and First-Order List Functions

On the Elementary Affine Lambda-Calculus with and Without Fixed Points

Modeling Reduplication with 2-way Finite-State Transducers

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