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A Class of Rational Trace Relations Closed Under Composition

Author Dietrich Kuske

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Author Details

Dietrich Kuske
  • Technische Universität Ilmenau, Germany

Acknowledgements

I want to thank the anonymous reviewers whose knowledgeable comments led to a substantial improvement of this paper. This applies in particular to one deep review that pointed out the central role of the composition and its commutation with the natural homomorphism which resulted in clearer and more conceptional proofs.

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Dietrich Kuske. A Class of Rational Trace Relations Closed Under Composition. In 43rd IARCS Annual Conference on Foundations of Software Technology and Theoretical Computer Science (FSTTCS 2023). Leibniz International Proceedings in Informatics (LIPIcs), Volume 284, pp. 20:1-20:20, Schloss Dagstuhl – Leibniz-Zentrum für Informatik (2023) https://doi.org/10.4230/LIPIcs.FSTTCS.2023.20

Abstract

Rational relations on words form a well-studied and often applied notion. While the definition in trace monoids is immediate, they have not been studied in this more general context. A possible reason is that they do not share the main useful properties of rational relations on words. To overcome this unfortunate limitation, this paper proposes a restricted class of rational relations, investigates its properties, and applies the findings to systems equipped with a pushdown that does not hold a word but a trace.

Subject Classification

ACM Subject Classification
  • Theory of computation → Formal languages and automata theory
Keywords
  • rational relations
  • Mazurkiewicz traces
  • preservation of rationality and recognizability

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References

  1. V. Bárány, E. Grädel, and S. Rubin. Automata-based presentations of infinite structures. In Finite and Algorithmic Model Theory, pages 1-76. Cambridge University Press, 2011. Google Scholar
  2. P. Barceló, D. Figueira, and L. Libkin. Graph logics with rational relations and the generalized intersection problem. In LICS'12, pages 115-124. IEEE Computer Society, 2012. Google Scholar
  3. W. Bekker and V. Goranko. Symbolic model checking of tense logics on rational Kripke models. In ILC'07, Lecture Notes in Comp. Sciecne, pages 2-20. Springer, 2009. Google Scholar
  4. J. Berstel. Transductions and context-free languages. Teubner Studienbücher, Stuttgart, 1979. Google Scholar
  5. B. Bollig. Formal Models of Communicating Systems - Languages, Automata, and Monadic Second-Order Logic. Springer, 2006. Google Scholar
  6. A. Bouajjani, J. Esparza, and O. Maler. Reachability analysis of pushdown automata: Application to model-checking. In CONCUR'97, Lecture Notes in Mathematics, vol. 1243. Springer, 1997. Google Scholar
  7. A. Carayol and A. Meyer. Context-sensitive languages, rational graphs and determinism. Log. Methods Comput. Sci., 2(2), 2006. Google Scholar
  8. A. Carayol and C. Morvan. On rational trees. In CSL'06, Lecture Notes in Computer Science vol. 4207, pages 225-239. Springer, 2006. Google Scholar
  9. P. Cartier and D. Foata. Problèmes combinatoires de commutation et réarrangements. Lecture Notes in Mathematics vol. 85. Springer, Berlin - Heidelberg - New York, 1969. Google Scholar
  10. D. Caucal. On the regular structure of prefix rewriting. Theoretical Computer Science, 106:61-86, 1992. Google Scholar
  11. V. Diekert and G. Rozenberg. The Book of Traces. World Scientific Publ. Co., 1995. Google Scholar
  12. M. Droste, P. Gastin, and D. Kuske. Asynchronous cellular automata for pomsets. Theoretical Computer Science, 247:1-38, 2000. (Fundamental study). Google Scholar
  13. M. Droste and D. Kuske. Recognizable and logically definable languages of infinite computations in concurrent automata. International Journal of Foundations of Computer Science, 9:295-314, 1998. Google Scholar
  14. S. Eilenberg. Automata, Languages and Machines vol. A. Academic Press, New York, 1974. Google Scholar
  15. C.C. Elgot and G. Mezei. On relations defined by generalized finite automata. IBM J. Res. Develop., 9:47-65, 1965. Google Scholar
  16. A. Finkel, B. Willems, and P. Wolper. A direct symbolic approach to model checking pushdown systems. Electronic Notes in Theoretical Computer Science, 9:27-37, 1997. Google Scholar
  17. Ch. Frougny and J. Sakarovitch. Synchronized rational relations of finite and infinite words. Theoretical Computer Science, 108:45-82, 1993. Google Scholar
  18. E. Grädel. Automatic structures: Twenty years later. In LICS '20, pages 21-34. ACM, 2020. Google Scholar
  19. J. H. Johnson. Rational equivalence relations. Theor. Comput. Sci., 47(3):39-60, 1986. Google Scholar
  20. J. H. Johnson. Uniformizing rational relations for natural language applications using weighted determinization. In CIAA'10, Lecture Notes in Computer Science vol. 6482, pages 173-180. Springer, 2010. Google Scholar
  21. S.C. Kleene. Representation of events in nerve nets and finite automata. In C.E. Shannon and J. McCarthy, editors, Automata Studies, Annals of Mathematics Studies vol. 34, pages 3-40. Princeton University Press, 1956. Google Scholar
  22. Ch. Köcher. Verification of Automata with Storage Mechanisms. TU Ilmenau, 2022. Doctoral dissertation. Google Scholar
  23. Ch. Köcher and D. Kuske. Forwards- and backwards-reachability for cooperating multi-pushdown systems. In FCT'23, Lecture Notes in Comp. Science vol. 14252, pages 318-332. Springer, 2023. Google Scholar
  24. D. Kuske. The subtrace order and counting first-order logic. In CSR'20, Lecture Notes in Comp. Science vol. 12159, pages 289-302. Springer, 2020. Google Scholar
  25. D. Kuske and A. Muscholl. Communicating automata. In J.-E. Pin, editor, Handbook of Automata Theory, volume 2, pages 1147-1188. EMS Press, 2021. Google Scholar
  26. A. Mazurkiewicz. Concurrent program schemes and their interpretation. Technical report, DAIMI Report PB-78, Aarhus University, 1977. Google Scholar
  27. C. Morvan. On rational graphs. In FOSSACS'00, Lecture Notes in Comp. Science vol. 1784, pages 252-266. Springer, 2000. Google Scholar
  28. C. Morvan and C. Stirling. Rational graphs trace context-sensitive languages. In MFCS'01, Lecture Notes in Comp. Science vol. 2136, pages 548-559. Springer, 2001. Google Scholar
  29. A. Muscholl and H. Petersen. A note on the commutative closure of star-free languages. Inf. Process. Lett., 57(2):71-74, 1996. Google Scholar
  30. M. Nivat. Transductions des langages de Chomsky. Ann. Inst. Fourier, 18(1):339-456, 1968. Google Scholar
  31. J.-E. Pin. Finite automata. In J.-E. Pin, editor, Handbook of Automata Theory, pages 3-38. European Mathematical Society Publishing House, Zürich, Switzerland, 2021. Google Scholar
  32. Sasha Rubin. Automatic structures. In J.-E. Pin, editor, Handbook of Automata Theory, pages 1031-1070. EMS Press, 2021. Google Scholar
  33. J. Sakarovitch. The "last" decision problem for rational trace languages. In LATIN'92, Lecture Notes in Comp. Science vol. 583, pages 460-473. Springer, 1992. Google Scholar
  34. J. Sakarovitch. Elements of Automata Theory. Cambridge University Press, 2009. Google Scholar
  35. W. Thomas. A short introduction to infinite automata. In DLT'01, Lecture Notes in Comp. Science vol. 2295, pages 130-144. Springer, 2002. Google Scholar
  36. W. Zielonka. Notes on finite asynchronous automata. R.A.I.R.O. - Informatique Théorique et Applications, 21:99-135, 1987. Google Scholar
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