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Quantum Finite Automata and Probabilistic Reversible Automata: R-trivial Idempotent Languages

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Mathematical Foundations of Computer Science 2011 (MFCS 2011)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 6907))

Abstract

We study the recognition of \(\mathcal{R}\)-trivial idempotent (\(\mathcal{R}_1\)) languages by various models of “decide-and-halt” quantum finite automata (QFA) and probabilistic reversible automata (DH-PRA). We introduce bistochastic QFA (MM-BQFA), a model which generalizes both Nayak’s enhanced QFA and DH-PRA. We apply tools from algebraic automata theory and systems of linear inequalities to give a complete characterization of \(\mathcal{R}_1\) languages recognized by all these models. We also find that “forbidden constructions” known so far do not include all of the languages that cannot be recognized by measure-many QFA.

Supported by the Latvian Council of Science, grant No. 09.1570 and by the European Social Fund, contract No. 2009/0216/1DP/1.1.1.2.0/09/APIA/VIAA/044. Unabridged version of this article is available at http://arxiv.org/abs/1106.2530.

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Authors and Affiliations

  1. Faculty of Computing, University of Latvia, Raiņa bulv. 19, Riga, LV-1586, Latvia

    Marats Golovkins, Maksim Kravtsev & Vasilijs Kravcevs

Authors
  1. Marats Golovkins
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  2. Maksim Kravtsev
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  3. Vasilijs Kravcevs
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Editors and Affiliations

  1. Institute of Informatics, University of Warsaw, ul. Banacha 2, 02-097, Warsaw, Poland

    Filip Murlak  & Piotr Sankowski  & 

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Golovkins, M., Kravtsev, M., Kravcevs, V. (2011). Quantum Finite Automata and Probabilistic Reversible Automata: R-trivial Idempotent Languages. In: Murlak, F., Sankowski, P. (eds) Mathematical Foundations of Computer Science 2011. MFCS 2011. Lecture Notes in Computer Science, vol 6907. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-22993-0_33

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  • DOI: https://doi.org/10.1007/978-3-642-22993-0_33

  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-642-22992-3

  • Online ISBN: 978-3-642-22993-0

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