skip to main content
research-article

The Hilbert method for transducer equivalence

Published: 19 February 2019 Publication History

Abstract

This Hilbert Method, as discussed in this paper, is the idea to encode combinatorial objects used by automata, such as words or trees, into algebraic objects, such as numbers and polynomials, and to reason about the latter using results about polynomials like Hilbert's Basis Theorem. A typical application of the method is deciding of equivalence for string-to-string transducers that use registers.

References

[1]
M H Albert and J Lawrence. 1985. A proof of Ehrenfeucht's Conjecture. Theoretical Computer Science 41 (1985), 121--123.
[2]
Rajeev Alur and Pavol Cerný. 2010. Expressiveness of streaming string transducers. FSTTCS (2010).
[3]
Michael Benedikt, Timothy Duff, Aditya Sharad, and James Worrell. 2017. Polynomial automata - Zeroness and applications. LICS (2017), 1--12.
[4]
Anna M Bigatti, Philippe Gimenez, and Eduardo Sáenz-de Cabezón (Eds.). 2017. Computations and Combinatorics in Commutative Algebra. Lecture Notes in Mathematics, Vol. 2176. Springer International Publishing, Cham.
[5]
Adrien Boiret, Radoslaw Piórkowski, and Janusz Schmude. 2018. Reducing Transducer Equivalence to Register Automata Problems Solved by" Hilbert Method". In 38th IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2018). Schloss Dagstuhl-Leibniz-Zentrum fuer Informatik.
[6]
Mikołaj Bojańczyk and Wojciech Czerwiński. Automata Toolbox. (????). https://www.mimuw.edu.pl/~bojan/upload/reduced-may-25.pdf
[7]
Karel Culik II and Juhani Karhumäki. 1986. The equivalence of finite valued transducers (on HDT0L languages) is decidable. Theoretical Computer Science 47 (1986), 71--84.
[8]
Emmanuel Filiot and Pierre-Alain Reynier. 2017. Copyful Streaming String Transducers. In International Workshop on Reachability Problems. Springer, 75--86.
[9]
Hugo Gimbert and Youssouf Oualhadj. 2010. Probabilistic automata on finite words: Decidable and undecidable problems. In International Colloquium on Automata, Languages, and Programming. Springer, 527--538.
[10]
Helmut Seidl, Sebastian Maneth, and Gregor Kemper. 2015. Equivalence of Deterministic Top-Down Tree-to-String Transducers is Decidable. In 2015 IEEE 56th Annual Symposium on Foundations of Computer Science (FOCS). IEEE, 943--962.
[11]
Alfred Tarski. 1951. A Decision Method for Elementary Algebra and Geometry.

Cited By

View all
  • (2024)Slice closures of indexed languages and word equations with counting constraintsProceedings of the 39th Annual ACM/IEEE Symposium on Logic in Computer Science10.1145/3661814.3662134(1-12)Online publication date: 8-Jul-2024
  • (2024)Finite-valued Streaming String TransducersProceedings of the 39th Annual ACM/IEEE Symposium on Logic in Computer Science10.1145/3661814.3662095(1-14)Online publication date: 8-Jul-2024
  • (2023)Characterizing attributed tree translations in terms of macro tree transducersTheoretical Computer Science10.1016/j.tcs.2023.113943963:COnline publication date: 26-Jun-2023

Recommendations

Comments

Information & Contributors

Information

Published In

cover image ACM SIGLOG News
ACM SIGLOG News  Volume 6, Issue 1
January 2019
39 pages
EISSN:2372-3491
DOI:10.1145/3313909
Issue’s Table of Contents

Publisher

Association for Computing Machinery

New York, NY, United States

Publication History

Published: 19 February 2019
Published in SIGLOG Volume 6, Issue 1

Check for updates

Qualifiers

  • Research-article

Contributors

Other Metrics

Bibliometrics & Citations

Bibliometrics

Article Metrics

  • Downloads (Last 12 months)7
  • Downloads (Last 6 weeks)0
Reflects downloads up to 20 Jan 2025

Other Metrics

Citations

Cited By

View all
  • (2024)Slice closures of indexed languages and word equations with counting constraintsProceedings of the 39th Annual ACM/IEEE Symposium on Logic in Computer Science10.1145/3661814.3662134(1-12)Online publication date: 8-Jul-2024
  • (2024)Finite-valued Streaming String TransducersProceedings of the 39th Annual ACM/IEEE Symposium on Logic in Computer Science10.1145/3661814.3662095(1-14)Online publication date: 8-Jul-2024
  • (2023)Characterizing attributed tree translations in terms of macro tree transducersTheoretical Computer Science10.1016/j.tcs.2023.113943963:COnline publication date: 26-Jun-2023

View Options

Login options

View options

PDF

View or Download as a PDF file.

PDF

eReader

View online with eReader.

eReader

Media

Figures

Other

Tables

Share

Share

Share this Publication link

Share on social media