Quantum Büchi Automata
Abstract
Quantum finite automata (QFAs) have been extensively studied in the literature. In this paper, we define and systematically study quantum Büchi automata (QBAs) over infinite words to model the long-term behavior of quantum systems, which extend QFAs. We introduce the classes of $\omega$-languages recognized by QBAs in probable, almost sure, strict and non-strict threshold semantics. Several pumping lemmas and closure properties for QBAs are proved. Some decision problems for QBAs are investigated. In particular, we show that there are surprisingly only at most four substantially different classes of $\omega$-languages recognized by QBAs (out of uncountably infinite). The relationship between classical $\omega$-languages and QBAs is clarified using our pumping lemmas. We also find an $\omega$-language recognized by QBAs under the almost sure semantics, which is not $\omega$-context-free.
- Publication:
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arXiv e-prints
- Pub Date:
- April 2018
- DOI:
- 10.48550/arXiv.1804.08982
- arXiv:
- arXiv:1804.08982
- Bibcode:
- 2018arXiv180408982W
- Keywords:
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- Computer Science - Logic in Computer Science;
- Computer Science - Formal Languages and Automata Theory;
- Quantum Physics
- E-Print:
- Full final version. 40 pages, 1 figure, 2 tables. Removed [v1]'s disturbing acceptance for simplicity, so all QBAs in [v2] obeys non-disturbing acceptance