The paper investigates non-deterministic, probabilistic and quantum walks, from the perspective of coalgebras and monads. Non-deterministic and probabilistic walks are coalgebras of a monad (powerset and distribution), in an obvious manner. It is shown that also quantum walks are coalgebras of a new monad, involving additional control structure. This new monad is also used to describe Turing machines coalgebraically, namely as controlled ‘walks’ on a tape.


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Copyright information

© Springer-Verlag Berlin Heidelberg 2011

Authors and Affiliations

  • Bart Jacobs
    • 1
  1. 1.Institute for Computing and Information Sciences (iCIS)Radboud University NijmegenThe Netherlands

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