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Pebble Minimization of Polyregular Functions

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Nathan LhoteAuthors Info & Claims

LICS '20: Proceedings of the 35th Annual ACM/IEEE Symposium on Logic in Computer Science

Pages 703 - 712

https://doi.org/10.1145/3373718.3394804

Published: 08 July 2020 Publication History

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Abstract

We show that a polyregular word-to-word function is regular if and only its output size is at most linear in its input size. Moreover a polyregular function can be realized by: a transducer with two pebbles if and only if its output has quadratic size in its input, a transducer with three pebbles if and only if its output has cubic size in its input, etc.

Moreover the characterization is decidable and, given a polyregular function, one can compute a transducer realizing it with the minimal number of pebbles.

We apply the result to mso interpretations from words to words. We show that mso interpretations of dimension k exactly coincide with k-pebble transductions.

References

[1]

Rajeev Alur and Pavol Cerný. 2010. Expressiveness of streaming string transducers. In IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science, FSTTCS 2010, December 15-18, 2010, Chennai, India. 1--12. https://doi.org/10.4230/LIPIcs.FSTTCS. 2010.1

Crossref

Google Scholar

[2]

Rajeev Alur, Adam Freilich, and Mukund Raghothaman. 2014. Regular combinators for string transformations. In Joint Meeting of the Twenty-Third EACSL Annual Conference on Computer Science Logic (CSL) and the Twenty-Ninth Annual ACM/IEEE Symposium on Logic in Computer Science (LICS), CSL-LICS '14, Vienna, Austria, July 14-18, 2014, Thomas A. Henzinger and Dale Miller (Eds.). ACM, 9:1--9:10. https://doi.org/10. 1145/2603088.2603151

Digital Library

Google Scholar

[3]

Mikołaj Bojańczyk. 2018. Polyregular Functions. CoRR abs/1810.08760 (2018). arXiv:1810.08760 http://arxiv.org/abs/1810.08760

Google Scholar

[4]

Mikolaj Bojańczyk, Laure Daviaud, and Shankara Narayanan Krishna. 2018. Regular and First-Order List Functions. In Proceedings of the 33rd Annual ACM/IEEE Symposium on Logic in Computer Science, LICS 2018, Oxford, UK, July 09-12, 2018, Anuj Dawar and Erich Grädel (Eds.). ACM, 125--134. https://doi.org/10.1145/3209108.3209163

Digital Library

Google Scholar

[5]

Mikołaj Bojańczyk, Sandra Kiefer, and Nathan Lhote. 2019. String-to-String Interpretations With Polynomial-Size Output. In 46th International Colloquium on Automata, Languages, and Programming, ICALP 2019, July 9-12, 2019, Patras, Greece. (LIPIcs), Christel Baier, Ioannis Chatzigiannakis, Paola Flocchini, and Stefano Leonardi (Eds.), Vol. 132. Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik, 106:1--106:14. https: //doi.org/10.4230/LIPIcs.ICALP.2019.106

Crossref

Google Scholar

[6]

Joost Engelfriet and Hendrik Jan Hoogeboom. 2001. MSO definable string transductions and two-way finite-state transducers. ACM Trans. Comput. Log. 2, 2 (2001), 216--254. https://doi.org/10.1145/371316.371512

Digital Library

Google Scholar

[7]

Noa Globerman and David Harel. 1996. Complexity Results for Two-Way and Multi-Pebble Automata and their Logics. Theor. Comput. Sci. 169, 2 (1996), 161--184. https://doi.org/10.1016/S0304-3975(96)00119-3

Digital Library

Google Scholar

[8]

Tova Milo, Dan Suciu, and Victor Vianu. 2003. Typechecking for XML transformers. J. Comput. Syst. Sci. 66, 1 (2003), 66--97. https://doi.org/10.1016/S0022-0000(02)00030-2

Digital Library

Google Scholar

Cited By

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Jordon LMaguire PMoser P(2024)Pebble-depthTheoretical Computer Science10.1016/j.tcs.2024.1146381009:COnline publication date: 12-Sep-2024
https://dl.acm.org/doi/10.1016/j.tcs.2024.114638
Rawski JDolatian HHeinz JRaimy E(2023)Regular and polyregular theories of reduplicationGlossa: a journal of general linguistics10.16995/glossa.88858:1Online publication date: 6-Jan-2023
https://doi.org/10.16995/glossa.8885
Bojańczyk M(2023)On the Growth Rates of Polyregular Functions2023 38th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)10.1109/LICS56636.2023.10175808(1-13)Online publication date: 26-Jun-2023
https://doi.org/10.1109/LICS56636.2023.10175808
Show More Cited By

Index Terms

Pebble Minimization of Polyregular Functions
1. Theory of computation
  1. Formal languages and automata theory
    1. Automata extensions
      1. Transducers

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LICS '20: Proceedings of the 35th Annual ACM/IEEE Symposium on Logic in Computer Science

July 2020

986 pages

ISBN:9781450371049

DOI:10.1145/3373718

Conference Chairs:
Holger Hermanns,
Lijun Zhang,
Naoki Kobayashi,
General Chair:
Dale Miller

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Published: 08 July 2020

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LICS '20: 35th Annual ACM/IEEE Symposium on Logic in Computer Science

July 8 - 11, 2020

Saarbrücken, Germany

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LICS '20 Paper Acceptance Rate 69 of 174 submissions, 40%;

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Jordon LMaguire PMoser P(2024)Pebble-depthTheoretical Computer Science10.1016/j.tcs.2024.1146381009:COnline publication date: 12-Sep-2024
https://dl.acm.org/doi/10.1016/j.tcs.2024.114638
Rawski JDolatian HHeinz JRaimy E(2023)Regular and polyregular theories of reduplicationGlossa: a journal of general linguistics10.16995/glossa.88858:1Online publication date: 6-Jan-2023
https://doi.org/10.16995/glossa.8885
Bojańczyk M(2023)On the Growth Rates of Polyregular Functions2023 38th Annual ACM/IEEE Symposium on Logic in Computer Science (LICS)10.1109/LICS56636.2023.10175808(1-13)Online publication date: 26-Jun-2023
https://doi.org/10.1109/LICS56636.2023.10175808
Bojanczyk M(2022)Transducers of polynomial growthProceedings of the 37th Annual ACM/IEEE Symposium on Logic in Computer Science10.1145/3531130.3533326(1-27)Online publication date: 2-Aug-2022
https://dl.acm.org/doi/10.1145/3531130.3533326

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Polyregular Functions: Characterisations and Refutations

Pebble minimization: the last theorems

Minimization and Characterizations for Biautomata

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