Pebble Minimization of Polyregular Functions

Lhote, Nathan

doi:10.1145/3373718.3394804

Cited by 6 publications

(3 citation statements)

References 31 publications

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“…Rational functions are computed by 1-way FSTs, and regular functions by 2-way FSTs (Engelfriet and Hoogeboom, 2001). 2 They share the following property in terms of growth rates (Lhote, 2020). Theorem 1.…”

Section: Illustrating Growth Size Of Recursive Prosodymentioning

confidence: 98%

Recursive prosody is not finite-state

Dolatian¹,

Santo²,

Graf³

2021

Proceedings of the 18th SIGMORPHON Workshop on Computational Research in Phonetics, Phonology, and Morphology

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This paper investigates bounds on the generative capacity of prosodic processes, by focusing on the complexity of recursive prosody in coordination contexts in English (Wagner, 2010). Although all phonological processes and most prosodic processes are computationally regular string languages, we show that recursive prosody is not. The output string language is instead parallel multiple context-free (Seki et al., 1991). We evaluate the complexity of the pattern over strings, and then move on to a characterization over trees that requires the expressivity of multi bottom-up tree transducers. In doing so, we provide a foundation for future mathematically grounded investigations of the syntax-prosody interface.

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Section: Illustrating Growth Size Of Recursive Prosodymentioning

confidence: 98%

Recursive prosody is not finite-state

Dolatian¹,

Santo²,

Graf³

2021

Proceedings of the 18th SIGMORPHON Workshop on Computational Research in Phonetics, Phonology, and Morphology

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“…For polyregular functions, the size of the output string can grow polynomially with respect to the size of the input string |w|, i.e. (|w| n ) (Bojańczyk et al 2019;Lhote 2020). The polynomial growth property enables many equivalent characterizations of polyregular functions, in terms of logic, algebra, and automata (Bojanczyk 2022).…”

Section: Polyregular Computation and Reduplicationmentioning

confidence: 99%

Regular and polyregular theories of reduplication

Rawski

Dolatian

Heinz

et al. 2023

Glossa: A Journal of General Linguistics

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We explore the generative capacity of morphological theories of reduplication. We computationally classify theories of reduplication using a hierarchy of string-to-string function classes. Reduplication as a process requires only the regular class of functions. We show that various morphological theories necessarily treat it as a more expressive polyregular function, while others maintain regularity. We discuss the significance of this formal result for reduplicative functions and recognition.

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“…While equivalent to two-way finite-state acceptors, pebble transducers are much more powerful. Specifically, a recent result by Lhote demonstrates that a polyregular function has output of size O(n k+1 ) in relation to an input of length n if and only if the function can be performed by a k-pebble transducer [20].…”

Section: Introductionmentioning

confidence: 99%

Pebble-Depth

Jordon¹,

Moser²

2020

Preprint

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In this paper we introduce a new formulation of Bennett's logical depth based on pebble transducers. This notion is defined based on the difference between the minimal length descriptional complexity of strings from the perspective of finite-state transducers and pebble transducers. Our notion of pebble-depth satisfies the three fundamental properties of depth: i.e. easy sequences and random sequences are not deep, and the existence of a slow growth law. We also compare pebble-depth to other depth notions based on finite-state transducers, pushdown compressors and the Lempel-Ziv 78 compression algorithm. We first demonstrate how there exists a normal pebble-deep sequence even though there is no normal finite-statedeep sequence. We next build a sequence which has a pebble-depth level of roughly 1, a pushdown-depth level of roughly 1/2 and a finite-state-depth level of roughly 0. We then build a sequence which has pebble-depth level of roughly 1/2 and Lempel-Ziv-depth level of roughly 0.

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Pebble Minimization of Polyregular Functions

Cited by 6 publications

References 31 publications

Recursive prosody is not finite-state

Recursive prosody is not finite-state

Regular and polyregular theories of reduplication

Pebble-Depth

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