A Circuit Complexity Approach to Transductions

  • Michaël CadilhacEmail author
  • Andreas Krebs
  • Michael Ludwig
  • Charles Paperman
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 9234)


Low circuit complexity classes and regular languages exhibit very tight interactions that shade light on their respective expressiveness. We propose to study these interactions at a functional level, by investigating the deterministic rational transductions computable by constant-depth, polysize circuits. To this end, a circuit framework of independent interest that allows variable output length is introduced. Relying on it, there is a general characterization of the set of transductions realizable by circuits. It is then decidable whether a transduction is definable in \(\mathrm{AC}^0\) and, assuming a well-established conjecture, the same for \(\mathrm{ACC}^0\).


Regular Language Surjective Morphism Input Length Output Gate Output Length 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



We thank Michael Blondin, Michael Hahn, and the referees.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2015

Authors and Affiliations

  • Michaël Cadilhac
    • 1
    Email author
  • Andreas Krebs
    • 1
  • Michael Ludwig
    • 1
  • Charles Paperman
    • 2
  1. 1.Wilhelm Schickard InstitutUniversität TübingenTübingenGermany
  2. 2.University of Warsaw and Warsaw Center of Mathematics and Computer ScienceWarsawPoland

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