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Single-Use Automata and Transducers for Infinite Alphabets

Authors Mikołaj Bojańczyk, Rafał Stefański

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ACM Subject Classification
  • Theory of computation → Formal languages and automata theory
Keywords
  • Automata
  • semigroups
  • data words
  • orbit-finite sets

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Abstract

Our starting point are register automata for data words, in the style of Kaminski and Francez. We study the effects of the single-use restriction, which says that a register is emptied immediately after being used. We show that under the single-use restriction, the theory of automata for data words becomes much more robust. The main results are: (a) five different machine models are equivalent as language acceptors, including one-way and two-way single-use register automata; (b) one can recover some of the algebraic theory of languages over finite alphabets, including a version of the Krohn-Rhodes Theorem; (c) there is also a robust theory of transducers, with four equivalent models, including two-way single use transducers and a variant of streaming string transducers for data words. These results are in contrast with automata for data words without the single-use restriction, where essentially all models are pairwise non-equivalent.

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Mikołaj Bojańczyk and Rafał Stefański. Single-Use Automata and Transducers for Infinite Alphabets. In 47th International Colloquium on Automata, Languages, and Programming (ICALP 2020). Leibniz International Proceedings in Informatics (LIPIcs), Volume 168, pp. 113:1-113:14, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2020) https://doi.org/10.4230/LIPIcs.ICALP.2020.113

Author Details

Mikołaj Bojańczyk
  • Institute of Informatics, University of Warsaw, Poland
Rafał Stefański
  • Institute of Informatics, University of Warsaw, Poland

Funding

Supported by the European Research Council under the European Unions Horizon 2020 research and innovation programme (ERC consolidator grant LIPA, agreement no. 683080).

References

  1. Ginzburg Abraham. Algebraic Theory of Automata. Elsevier, 1968. Google Scholar
  2. Rajeev Alur and Pavol Černý. Expressiveness of streaming string transducers. In Foundations of Software Technology and Theoretical Computer Science, FSTTCS 2010, Chennai, India, volume 8 of LIPIcs, pages 1-12. Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik, 2010. Google Scholar
  3. Henrik Björklund and Thomas Schwentick. On notions of regularity for data languages. Theoretical Computer Science, 411(4):702-715, January 2010. Google Scholar
  4. Mikołaj Bojańczyk. Automata for Data Words and Data Trees. In Christopher Lynch, editor, Rewriting Techniques and Applications, RTA, Edinburgh, Scottland, UK, volume 6 of LIPIcs, pages 1-4. Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik, 2010. Google Scholar
  5. Mikołaj Bojańczyk. Nominal Monoids. Theory Comput. Syst., 53(2):194-222, 2013. Google Scholar
  6. Mikołaj Bojańczyk. Slightly infinite sets, 2019. URL: https://www.mimuw.edu.pl/~bojan/paper/atom-book [cited version of September 11, 2019]. URL: https://www.mimuw.edu.pl/~bojan/paper/atom-book.
  7. Mikołaj Bojańczyk, Laure Daviaud, and Shankara Narayanan Krishna. Regular and First-Order List Functions. In Logic in Computer Science, LICS, Oxford, UK, pages 125-134. ACM, 2018. Google Scholar
  8. Michal Chytil and Vojtech Jákl. Serial Composition of 2-Way Finite-State Transducers and Simple Programs on Strings. In International Colloquium on Automata, Languages and Programming, ICALP, Turku, Finland, volume 52 of Lecture Notes in Computer Science, pages 135-147. Springer, 1977. Google Scholar
  9. Thomas Colcombet, Clemens Ley, and Gabriele Puppis. Logics with rigidly guarded data tests. Logical Methods in Computer Science, 11(3), 2015. Google Scholar
  10. Luc Dartois, Paulin Fournier, Ismaël Jecker, and Nathan Lhote. On reversible transducers. In International Colloquium on Automata, Languages and Programming, ICALP, Warsaw, Poland, volume 80 of LIPIcs, pages 113:1-113:12. Schloss Dagstuhl - Leibniz-Zentrum fuer Informatik, 2017. Google Scholar
  11. Emmanuel Filiot and Pierre-Alain Reynier. Transducers, logic and algebra for functions of finite words. SIGLOG News, 3(3):4-19, 2016. Google Scholar
  12. Emmanuel Filiot and Pierre-Alain Reynier. Copyful Streaming String Transducers. In Matthew Hague and Igor Potapov, editors, Reachability Problems, RP , London, UK, volume 10506 of Lecture Notes in Computer Science, pages 75-86. Springer, 2017. Google Scholar
  13. Michael Kaminski and Nissim Francez. Finite-Memory Automata. Theor. Comput. Sci., 134(2):329-363, 1994. Google Scholar
  14. Kenneth Krohn and John Rhodes. Algebraic theory of machines. i. prime decomposition theorem for finite semigroups and machines. Transactions of the American Mathematical Society, 116:450-450, 1965. Google Scholar
  15. Frank Neven, Thomas Schwentick, and Victor Vianu. Finite state machines for strings over infinite alphabets. ACM Trans. Comput. Log., 5(3):403-435, 2004. Google Scholar
  16. J. C. Shepherdson. The reduction of two-way automata to one-way automata. IBM Journal of Research and Development, 3(2):198-200, April 1959. Google Scholar
  17. Imre Simon. Factorization forests of finite height. Theoretical Computer Science, 72(1):65-94, 1990. Google Scholar
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