scholarly journals On the Circuit Complexity of Perfect Hashing

2011 ◽  
pp. 26-29
Author(s):  
Oded Goldreich ◽  
Avi Wigderson
Keyword(s):  
Circuit Complexity ◽  
Perfect Hashing

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

A letter oriented minimal perfect hashing function

1982 ◽  
Vol 17 (9) ◽  
pp. 18-27 ◽  
Author(s):  
Curtis R. Cook ◽  
R. R. Oldehoeft
Keyword(s):  
Hashing Function ◽  
Perfect Hashing

scholarly journals Computational and Proof Complexity of Partial String Avoidability

2021 ◽  
Vol 13 (1) ◽  
pp. 1-25
Author(s):  
Dmitry Itsykson ◽  
Alexander Okhotin ◽  
Vsevolod Oparin
Keyword(s):  
Lower Bounds ◽  
Circuit Complexity ◽  
Conjunctive Normal Form ◽  
Proof Complexity ◽  
Proof Systems ◽  
Finite Set ◽  
Propositional Proof Systems ◽  
Classical Proof ◽  
Exponential Size ◽  
Infinite String

The partial string avoidability problem is stated as follows: given a finite set of strings with possible “holes” (wildcard symbols), determine whether there exists a two-sided infinite string containing no substrings from this set, assuming that a hole matches every symbol. The problem is known to be NP-hard and in PSPACE, and this article establishes its PSPACE-completeness. Next, string avoidability over the binary alphabet is interpreted as a version of conjunctive normal form satisfiability problem, where each clause has infinitely many shifted variants. Non-satisfiability of these formulas can be proved using variants of classical propositional proof systems, augmented with derivation rules for shifting proof lines (such as clauses, inequalities, polynomials, etc.). First, it is proved that there is a particular formula that has a short refutation in Resolution with a shift rule but requires classical proofs of exponential size. At the same time, it is shown that exponential lower bounds for classical proof systems can be translated for their shifted versions. Finally, it is shown that superpolynomial lower bounds on the size of shifted proofs would separate NP from PSPACE; a connection to lower bounds on circuit complexity is also established.

A FAST CHINESE CHARACTERS ACCESSING TECHNIQUE USING MANDARIN PHONETIC TRANSCRIPTIONS

1988 ◽  
Vol 02 (01) ◽  
pp. 105-137 ◽  
Author(s):  
C.C. CHANG ◽  
H.C. WU
Keyword(s):  
Main Idea ◽  
Chinese Characters ◽  
One To One ◽  
Hashing Function ◽  
Perfect Hashing ◽  
The Way

In this paper, we consider the problem of how to design a minimal perfect hashing function which is suitable for the Mandarin Phonetic Symbols system. Our main idea is inspired by Chang’s letter-oriented minimal perfect hashing scheme. By using our hashing function, 1303 Mandarin phonetic symbol transcriptions will be hashed to 1303 locations in the way of one-to-one correspondence.

A Better-Than-3n Lower Bound for the Circuit Complexity of an Explicit Function

2016 ◽  
Author(s):  
Magnus Gausdal Find ◽  
Alexander Golovnev ◽  
Edward A. Hirsch ◽  
Alexander S. Kulikov
Keyword(s):  
Lower Bound ◽  
Circuit Complexity ◽  
Explicit Function ◽  
Better Than
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