WFSM Auto-intersection and Join Algorithms

  • A. Kempe
  • J. -M. Champarnaud
  • F. Guingne
  • F. Nicart
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4002)


The join of two n-ary string relations is a main operation regarding to applications. n-Ary rational string relations are realized by weighted finite-state machines with n tapes. We provide an algorithm that computes the join of two machines via a more simple operation, the auto-intersection. The two operations generally do not preserve rationality. A delay-based algorithm is described for the case of a single tape pair, as well as the class of auto-intersections that it handles. It is generalized to multiple tape pairs and some enhancements are discussed.


Error Code Multiple Pair String Relation Successful Path Positive Delay 
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  1. 1.
    Rabin, M.O., Scott, D.: Finite automata and their decision problems. IBM Journal of Research and Development 3, 114–125 (1959)MathSciNetCrossRefMATHGoogle Scholar
  2. 2.
    Elgot, C.C., Mezei, J.E.: On relations defined by generalized finite automata. IBM Journal of Research and Development 9, 47–68 (1965)MathSciNetCrossRefMATHGoogle Scholar
  3. 3.
    Kay, M.: Nonconcatenative finite-state morphology. In: Proc. 3rd Int. Conf. EACL, Copenhagen, Denmark, pp. 2–10 (1987)Google Scholar
  4. 4.
    Harju, T., Karhumäki, J.: The equivalence problem of multitape finite automata. Theoretical Computer Science 78, 347–355 (1991)MathSciNetCrossRefMATHGoogle Scholar
  5. 5.
    Kaplan, R.M., Kay, M.: Regular models of phonological rule systems. Computational Linguistics 20, 331–378 (1994)Google Scholar
  6. 6.
    Kempe, A., Champarnaud, J.M., Eisner, J.: A note on join and auto-intersection of n-ary rational relations. In: Watson, B., Cleophas, L. (eds.) Proc. Eindhoven FASTAR Days. Number 04–40 in TU/e CS TR, Eindhoven, Netherlands, pp. 64–78 (2004)Google Scholar
  7. 7.
    Kiraz, G.A.: Multitiered nonlinear morphology using multitape finite automata: a case study on Syriac and Arabic. Computational Lingistics 26, 77–105 (2000)CrossRefGoogle Scholar
  8. 8.
    Eilenberg, S.: Automata, Languages, and Machines, vol. A. Academic Press, San Diego (1974)MATHGoogle Scholar
  9. 9.
    Kuich, W., Salomaa, A.: Semirings, Automata, Languages. EATCS Monographs on Theoretical Computer Science, vol. (5). Springer, Berlin, Germany (1986)CrossRefMATHGoogle Scholar
  10. 10.
    Mohri, M., Pereira, F.C.N., Riley, M.: A rational design for a weighted finite-state transducer library. In: Wood, D., Yu, S. (eds.) WIA 1997. LNCS, vol. 1436, pp. 144–158. Springer, Heidelberg (1998)CrossRefGoogle Scholar
  11. 11.
    Kempe, A., Guingne, F., Nicart, F.: Algorithms for weighted multi-tape automata. Research report 2004/031, Xerox Research Centre Europe, Meylan, France (2004)Google Scholar
  12. 12.
    Rosenberg, A.L.: On n-tape finite state acceptors. In: IEEE Symposium on Foundations of Computer Science (FOCS), pp. 76–81 (1964)Google Scholar
  13. 13.
    Eisner, J.: Parameter estimation for probabilistic finite-state transducers. In: Proc. of the 40th Annual Meeting of the Association for Computational Linguistics, Philadelphia (2002)Google Scholar
  14. 14.
    Kempe, A.: NLP applications based on weighted multi-tape automata. In: Proc. 11th Conf. TALN, Fes, Morocco, pp. 253–258 (2004)Google Scholar
  15. 15.
    Kempe, A., Champarnaud, J.M., Eisner, J., Guingne, F., Nicart, F.: A class of rational n-WFSM auto-intersections. In: Farré, J., Litovsky, I., Schmitz, S. (eds.) CIAA 2005. LNCS, vol. 3845, pp. 188–198. Springer, Heidelberg (2006)CrossRefGoogle Scholar
  16. 16.
    Frougny, C., Sakarovitch, J.: Synchronized rational relations of finite and infinite words. Theoretical Computer Science 108, 45–82 (1993)MathSciNetCrossRefMATHGoogle Scholar
  17. 17.
    Mohri, M.: Edit-distance of weighted automata. In: Champarnaud, J.-M., Maurel, D. (eds.) CIAA 2002. LNCS, vol. 2608, pp. 1–23. Springer, Heidelberg (2003)CrossRefGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2006

Authors and Affiliations

  • A. Kempe
    • 1
  • J. -M. Champarnaud
    • 2
  • F. Guingne
    • 1
    • 3
  • F. Nicart
    • 1
    • 3
  1. 1.Grenoble LaboratoryXerox Research Centre EuropeMeylanFrance
  2. 2.PSI Laboratory (Université de Rouen, CNRS)Mont-Saint-AignanFrance
  3. 3.LIFAR Laboratory (Université de Rouen)Mont-Saint-AignanFrance

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