A Quantum Query Complexity Trichotomy for Regular Languages

2019 IEEE 60TH ANNUAL SYMPOSIUM ON FOUNDATIONS OF COMPUTER SCIENCE (FOCS 2019), pp. 942.0-965, 2019.

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Abstract:

We present a trichotomy theorem for the quantum query complexity of regular languages. Every regular language has quantum query complexity circle minus(1), (circle minus) over tilde(root n), or circle minus(n). The extreme uniformity of regular languages prevents them from taking any other asymptotic complexity. This is in contrast to eve...More

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