In computations realized by finite automata, a rich understanding has come from comparing the algebraic structure of the machines to the combinatorics of the languages being recognized. In this expository paper, we will first survey some basic ideas that have been useful in this model. In the second part, we sketch how this dual approach can be generalized to study some important class of boolean circuits, what results have been obtained, what questions are still open. The intuition gained in the simple model sometimes carry through, sometimes not, so that one has to be careful on what conjectures to make.


Solvable Group Wreath Product Regular Language Boolean Circuit Output Gate 
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© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Denis Thérien
    • 1
  1. 1.School of Computer ScienceMcGill UniversityMontréalCanada

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