Acta Informatica

, Volume 27, Issue 8, pp 749–780

On the valuedness of finite transducers

  • Andreas Weber

DOI: 10.1007/BF00264285

Cite this article as:
Weber, A. Acta Informatica (1990) 27: 749. doi:10.1007/BF00264285


We investigate the valuedness of finite transducers in connection with their inner structure. We show: The valuedness of a finite-valued nondeterministic generalized sequential machine (NGSM) M with n states and output alphabet Δ is at most the maximum of (1-⌊1/#Δ⌋) · (2k1· k3)n· nn·#Δn3·k4/3 and ⌊1/#Δ⌋·(2k2·k3·(1+k4))n·nn where k1≦6.25 and k2≦11.89 are constants and k3≧1 and k4≧0 are local structural parameters of M. There are two simple criteria which characterize the infinite valuedness of an NGSM. By these criteria, it is decidable in polynomial time whether or not an NGSM is infinite-valued. In both cases, #Δ > 1 and #Δ = 1, the above upper bound for the valuedness is almost optimal. By reduction, all results can be easily generalized to normalized finite transducers.

Copyright information

© Springer-Verlag 1990

Authors and Affiliations

  • Andreas Weber
    • 1
  1. 1.Fachbereich InformatikJ.W. Goethe-UniversitätFrankfurt am Main 11Federal Republic of Germany