Logarithmic Space and Permutations

@article{Seiller2016LogarithmicSA,
  title={Logarithmic Space and Permutations},
  author={Thomas Seiller and Cl{\'e}ment Aubert},
  journal={Inf. Comput.},
  year={2016},
  volume={248},
  pages={2-21}
}
In a recent work, Girard [1] proposed a new and innovative approach to computational complexity based on the proofs-as-programs correspondence. In a previous paper [2], the authors showed how Girard’s proposal succeeds in obtaining a new characterization of co-NL languages as a set of operators acting on a Hilbert Space. In this paper, we extend this work by showing that it is also possible to define a set of operators characterizing the class L of logarithmic space languages. 
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