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We present a trichotomy theorem for the quantum query complexity of regular languages.
Representations of events in nerve nets and finite automata
Stephen Cole Kleene · 1956
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Algebraic theory of machines. I. Prime decomposition theorem for finite semigroups and machines
Kenneth Krohn and John Rhodes · 1965
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On finite monoids having only trivial subgroups
Marcel Paul Schützenberger · 1965
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Hierarchies of memory limited computations
Richard Edwin Stearns, Juris Hartmanis, and Philip M Lewis · 1965
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Tense logic and the theory of linear order
Johan Anthony Wilem Kamp · 1968
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Counter-Free Automata (MIT research monograph no. 65)
Robert McNaughton and Seymour A Papert · 1971
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Automata, Languages, and Machines
Samuel Eilenberg · 1974
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Some simplified 𝖭𝖯 {\mathsf{NP}} -complete problems
Michael R Garey, David S Johnson, and Larry Stockmeyer · 1974
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Noncounting context-free languages
Stefano Crespi-Reghizzi, Giovanni Guida, and Dino Mandrioli · 1978
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Universality considerations in VLSI circuits
Leslie G Valiant · 1981
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Unbounded fan-in circuits and associative functions
Ashok K Chandra, Steven Fortune, and Richard Lipton · 1983
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A tight Ω ( log log n ) {\Omega}(\log\log n) -bound on the time for parallel RAM’s to compute nondegenerated boolean functions
Hans-Ulrich Simon · 1983
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Finite monoids and the fine structure of 𝖭𝖢 1 {\mathsf{NC}}^{1}
David A Barrington and Denis Thérien · 1988
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Regular languages are testable with a constant number of queries
Noga Alon, Michael Krivelevich, Ilan Newman, and Mario Szegedy · 2001
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Quantum lower bounds by polynomials
Robert Beals, Harry Buhrman, Richard Cleve, Michele Mosca, and Ronald de Wolf · 2001
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Andris Ambainis · 2002
Polynomial degree and lower bounds in quantum complexity: Collision and element distinctness with small range
Andris Ambainis · 2005
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Quantum lower bound for the collision problem with small range
Samuel Kutin · 2005
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Introduction to the Theory of Computation
Michael Sipser · 2006
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Span programs and quantum query complexity: The general adversary bound is nearly tight for every boolean function
Ben W Reichardt · 2009
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Quantum query complexity of minor-closed graph properties
Andrew M Childs and Robin Kothari · 2012
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Circuit complexity of properties of graphs with constant planar cutwidth
Kristoffer Arnsfelt Hansen, Balagopal Komarath, Jayalal Sarma, Sven Skyum, and Navid Talebanfard · 2014
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Complexity measures and decision tree complexity: a survey
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Quantum search on bounded-error inputs
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Pascal Tesson and Denis Thérien · 2003
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The space just above BQP
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Which regular expression patterns are hard to match?
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Quantum speedups for exponential-time dynamic programming algorithms
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