Behaviours of Unary Quantum Automata

  • Authors:

  • Maria Paola Bianchi;Beatrice Palano

  • Affiliations:

  • Dipartimento di Scienze dell'Informazione, Università degli Studi di Milano, via Comelico 39 - 20135 Milano - Italy. maria.bianchi@unimi.it;(Correspd.) Dipartimento di Scienze dell'Informazione, Università degli Studi di Milano, via Comelico 39 - 20135 Milano - Italy. palano@dsi.unimi.it

  • Venue:
  • Fundamenta Informaticae - Non-Classical Models of Automata and Applications
  • Year:
  • 2010

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Abstract

We study the stochastic events induced by MM-qfa's working on unary alphabets. We give two algorithms for unary MM-qfa's: the first computes the dimension of the ergodic and transient components of the non halting subspace, while the second tests whether the induced event is d-periodic. These algorithms run in polynomial time whenever the MM-qfa given in input has complex amplitudes with rational components. We also characterize the recognition power of unary MM-qfa's, by proving that any unary regular language can be accepted by a MM-qfa with constant cut point and isolation. Yet, the amount of states of the resulting MM-qfa is linear in the size of the corresponding minimal dfa. We also single out families of unary regular languages for which the size of the accepting MM-qfa's can be exponentially decreased.