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Cost Functions Definable by Min/Max Automata

Authors Thomas Colcombet, Denis Kuperberg, Amaldev Manuel, Szymon Torunczyk

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Keywords
  • distance automata
  • B-automata
  • regular cost functions
  • stabilisation monoids
  • decidability
  • min-automata
  • max-automata

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Abstract

Regular cost functions form a quantitative extension of regular languages that share the array of characterisations the latter possess. In this theory, functions are treated only up to preservation of boundedness on all subsets of the domain. In this work, we subject the well known distance automata (also called min-automata), and their dual max-automata to this framework, and obtain a number of effective characterisations in terms of logic, expressions and algebra.

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Thomas Colcombet, Denis Kuperberg, Amaldev Manuel, and Szymon Torunczyk. Cost Functions Definable by Min/Max Automata. In 33rd Symposium on Theoretical Aspects of Computer Science (STACS 2016). Leibniz International Proceedings in Informatics (LIPIcs), Volume 47, pp. 29:1-29:13, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2016) https://doi.org/10.4230/LIPIcs.STACS.2016.29

Author Details

Thomas Colcombet
Denis Kuperberg
Amaldev Manuel
Szymon Torunczyk

References

  1. Parosh Aziz Abdulla, Pavel Krcál, and Wang Yi. R-automata. In CONCUR 2008, volume 5201, pages 67-81, 2008. Google Scholar
  2. Rajeev Alur, Loris D'Antoni, Jyotirmoy V. Deshmukh, Mukund Raghothaman, and Yifei Yuan. Regular functions and cost register automata. In LICS 2013, pages 13-22, 2013. Google Scholar
  3. Mikolaj Bojanczyk. Weak MSO with the unbounding quantifier. Theory Comput. Syst., 48(3):554-576, 2011. Google Scholar
  4. Mikolaj Bojańczyk and Thomas Colcombet. Bounds in ω-regularity. In LICS 06, pages 285-296, 2006. Google Scholar
  5. Mikolaj Bojanczyk and Szymon Torunczyk. Deterministic automata and extensions of weak mso. In FSTTCS, pages 73-84, 2009. Google Scholar
  6. Thomas Colcombet. The theory of stabilisation monoids and regular cost functions. In Automata, Languages and Programming, Internatilonal Collogquium, ICALP 2009, Proceedings, Part II, pages 139-150, 2009. Google Scholar
  7. Thomas Colcombet. Fonctions régulières de coût. Habilitation thesis, Université Paris Diderot-Paris, 2013. Google Scholar
  8. Thomas Colcombet. Regular cost functions, part I: logic and algebra over words. Logical Methods in Computer Science, 9(3), 2013. Google Scholar
  9. Thomas Colcombet and Laure Daviaud. Approximate comparison of distance automata. In STACS 2013, volume 20 of LIPIcs, pages 574-585, 2013. Google Scholar
  10. Thomas Colcombet, Laure Daviaud, and Florian Zuleger. Size-change abstraction and max-plus automata. In MFCS 2014, volume 8634 of Lecture Notes in Computer Science, pages 208-219, 2014. Google Scholar
  11. Thomas Colcombet, Denis Kuperberg, and Sylvain Lombardy. Regular temporal cost functions. Automata, Languages and Programming, pages 563-574, 2010. Google Scholar
  12. Daniel Kirsten. Distance desert automata and the star height problem. ITA, 39(3):455-509, 2005. Google Scholar
  13. Daniel Krob. The equality problem for rational series with multiplicities in the tropical semiring is undecidable. Internat. J. Algebra Comput., 4(3):405-425, 1994. Google Scholar
  14. Denis Kuperberg. Linear temporal logic for regular cost functions. Logical Methods in Computer Science, 10(1), 2014. Google Scholar
  15. Martin Lang, Christof Löding, and Amaldev Manuel. Definability and transformations for cost logics and automatic structures. In MFCS 2014, volume 8634 of Lecture Notes in Computer Science, pages 390-401. Springer, 2014. Google Scholar
  16. M.P. Schützenberger. On finite monoids having only trivial subgroups. Information and Control, 8(2):190 - 194, 1965. Google Scholar
  17. Szymon Torunczyk. Languages of profinite words and the limitedness problem. PhD thesis, PhD thesis, University of Warsaw, 2011. Google Scholar
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