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A Circuit Complexity Approach to Transductions

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Mathematical Foundations of Computer Science 2015 (MFCS 2015)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9234))

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Abstract

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 \(\mathrm{ACC}^0\).

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Acknowledgment

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

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Authors and Affiliations

  1. Wilhelm Schickard Institut, Universität Tübingen, Tübingen, Germany

    Michaël Cadilhac, Andreas Krebs & Michael Ludwig

  2. University of Warsaw and Warsaw Center of Mathematics and Computer Science, Warsaw, Poland

    Charles Paperman

Authors
  1. Michaël Cadilhac
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  2. Andreas Krebs
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  3. Michael Ludwig
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  4. Charles Paperman
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Corresponding author

Correspondence to Michaël Cadilhac .

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Editors and Affiliations

  1. Università di Roma "Tor Vergata", Rome, Italy

    Giuseppe F Italiano

  2. Università degli Studi di Milano, Milan, Italy

    Giovanni Pighizzini

  3. University of Edinburgh, Edinburgh, United Kingdom

    Donald T. Sannella

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Cadilhac, M., Krebs, A., Ludwig, M., Paperman, C. (2015). A Circuit Complexity Approach to Transductions. In: Italiano, G., Pighizzini, G., Sannella, D. (eds) Mathematical Foundations of Computer Science 2015. MFCS 2015. Lecture Notes in Computer Science(), vol 9234. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-662-48057-1_11

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  • DOI: https://doi.org/10.1007/978-3-662-48057-1_11

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  • Print ISBN: 978-3-662-48056-4

  • Online ISBN: 978-3-662-48057-1

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