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Unary Probabilistic and Quantum Automata on Promise Problems

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Developments in Language Theory (DLT 2015)

Part of the book series: Lecture Notes in Computer Science ((LNTCS,volume 9168))

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Abstract

We continue the systematic investigation of probabilistic and quantum finite automata (PFAs and QFAs) on promise problems by focusing on unary languages. We show that bounded-error QFAs are more powerful than PFAs. But, in contrary to the binary problems, the computational powers of Las-Vegas QFAs and bounded-error PFAs are equivalent to deterministic finite automata (DFAs). Lastly, we present a new family of unary promise problems with two parameters such that when fixing one parameter QFAs can be exponentially more succinct than PFAs and when fixing the other parameter PFAs can be exponentially more succinct than DFAs.

The extended version of the paper that contains the missing proofs is [10].

Abuzer Yakaryılmaz— Yakaryılmaz was partially supported by CAPES with grant 88881.030338/2013-01.

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Correspondence to Aida Gainutdinova .

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Gainutdinova, A., Yakaryılmaz, A. (2015). Unary Probabilistic and Quantum Automata on Promise Problems. In: Potapov, I. (eds) Developments in Language Theory. DLT 2015. Lecture Notes in Computer Science(), vol 9168. Springer, Cham. https://doi.org/10.1007/978-3-319-21500-6_20

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  • DOI: https://doi.org/10.1007/978-3-319-21500-6_20

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-21499-3

  • Online ISBN: 978-3-319-21500-6

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