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

We study the recognition of R-trivial idempotent (R1) 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 R1 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.

preprint2011arXivOpen access
Marats GolovkinsMaksim KravtsevVasilijs Kravcevs
Formal Languages and Automata Theoryquant-ph
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Marats GolovkinsMaksim KravtsevVasilijs Kravcevs

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