Regular Languages and Circuit Complexity

1994 ◽  
pp. 155-178
Author(s):  
Howard Straubing
Keyword(s):  
Circuit Complexity ◽  
Regular Languages

Circuit Complexity of Regular Languages

2009 ◽  
Vol 45 (4) ◽  
pp. 865-879 ◽  
Author(s):  
Michal Koucký
Keyword(s):  
Circuit Complexity ◽  
Regular Languages

Learning Regular Languages from Positive Evidence

1998 ◽  
Author(s):  
Laura Firoiu ◽  
Tim Oates ◽  
Paul R. Cohen
Keyword(s):  
Regular Languages ◽  
Positive Evidence

Regular languages under F-gsm mappings

1987 ◽  
Vol 18 (3) ◽  
pp. 41-45
Author(s):  
A J Dos Reis
Keyword(s):  
Regular Languages

scholarly journals A framework for reducing the overhead of the quantum oracle for use with Grover’s algorithm with applications to cryptanalysis of SIKE

2020 ◽  
Vol 15 (1) ◽  
pp. 143-156
Author(s):  
Jean-François Biasse ◽  
Benjamin Pring
Keyword(s):  
Search Algorithm ◽  
Circuit Complexity ◽  
Quantum Circuit ◽  
Grover’S Algorithm ◽  
Search Problems ◽  
Trade Offs ◽  
Single Target ◽  
Grover's Algorithm ◽  
Quantum Oracle ◽  
The Cost

AbstractIn this paper we provide a framework for applying classical search and preprocessing to quantum oracles for use with Grover’s quantum search algorithm in order to lower the quantum circuit-complexity of Grover’s algorithm for single-target search problems. This has the effect (for certain problems) of reducing a portion of the polynomial overhead contributed by the implementation cost of quantum oracles and can be used to provide either strict improvements or advantageous trade-offs in circuit-complexity. Our results indicate that it is possible for quantum oracles for certain single-target preimage search problems to reduce the quantum circuit-size from $O\left(2^{n/2}\cdot mC\right)$ (where C originates from the cost of implementing the quantum oracle) to $O(2^{n/2} \cdot m\sqrt{C})$ without the use of quantum ram, whilst also slightly reducing the number of required qubits.This framework captures a previous optimisation of Grover’s algorithm using preprocessing [21] applied to cryptanalysis, providing new asymptotic analysis. We additionally provide insights and asymptotic improvements on recent cryptanalysis [16] of SIKE [14] via Grover’s algorithm, demonstrating that the speedup applies to this attack and impacting upon quantum security estimates [16] incorporated into the SIKE specification [14].

scholarly journals Circuit complexity in interacting QFTs and RG flows

2018 ◽  
Vol 2018 (10) ◽  
Author(s):  
Arpan Bhattacharyya ◽  
Arvind Shekar ◽  
Aninda Sinha
Keyword(s):  
Circuit Complexity
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