Circuit Complexity of k-Valued Logic Functions in One Infinite Basis

2019 ◽  
Vol 30 (1) ◽  
pp. 13-25
Author(s):  
V. V. Kochergin ◽  
A. V. Mikhailovich
Keyword(s):  
Circuit Complexity ◽  
Infinite Basis ◽  
Logic Functions

High-Density Memristor-CMOS Ternary Logic Family

2020 ◽  
Author(s):  
Xiaoyuan Wang ◽  
Pengfei Zhou ◽  
Jason Eshraghian ◽  
Chih-Yang Lin ◽  
Herbert Ho-Ching Iu ◽  
...  
Keyword(s):  
Indium Tin Oxide ◽  
Practical Implementation ◽  
Switching Speed ◽  
High Data ◽  
Fast Switching ◽  
Data Density ◽  
Order Of Magnitude ◽  
High Transconductance ◽  
Logic Functions ◽  
Magnitude Improvement

<div>This paper presents the first experimental demonstration</div><div>of a ternary memristor-CMOS logic family. We systematically</div><div>design, simulate and experimentally verify the primitive</div><div>logic functions: the ternary AND, OR and NOT gates. These are then used to build combinational ternary NAND, NOR, XOR and XNOR gates, as well as data handling ternary MAX and MIN gates. Our simulations are performed using a 50-nm process which are verified with in-house fabricated indium-tin-oxide memristors, optimized for fast switching, high transconductance, and low current leakage. We obtain close to an order of magnitude improvement in data density over conventional CMOS logic, and a reduction of switching speed by a factor of 13 over prior state-of-the-art ternary memristor results. We anticipate extensions of this work can realize practical implementation where high data density is of critical importance.</div>

scholarly journals Skyrmion Logic-In-Memory Architecture for Maximum/Minimum Search

Electronics ◽  
2021 ◽  
Vol 10 (2) ◽  
pp. 155
Author(s):  
Luca Gnoli ◽  
Fabrizio Riente ◽  
Marco Vacca ◽  
Massimo Ruo Roch ◽  
Mariagrazia Graziano
Keyword(s):  
High Efficiency ◽  
Digital Design ◽  
Control Logic ◽  
Minimum Number ◽  
Physical Simulations ◽  
Good Energy ◽  
Logic Functions ◽  
Time And Energy ◽  
Cmos Implementation ◽  
Maximum Minimum

In modern computing systems there is the need to utilize a large amount of data in maintaining high efficiency. Limited memory bandwidth, coupled with the performance gap between memory and logic, impacts heavily on algorithms performance, increasing the overall time and energy required for computation. A possible approach to overcome such limitations is Logic-In-Memory (LIM). In this paper, we propose a LIM architecture based on a non-volatile skyrmion-based recetrack memory. The architecture can be used as a memory or can perform advanced logic functions on the stored data, for example searching for the maximum/minimum number. The circuit has been designed and validated using physical simulations for the memory array together with digital design tools for the control logic. The results highlight the small area of the proposed architecture and its good energy efficiency compared with a reference CMOS implementation.

scholarly journals Training an asymmetric signal perceptron through reinforcement in an artificial chemistry

2014 ◽  
Vol 11 (93) ◽  
pp. 20131100 ◽  
Author(s):  
Peter Banda ◽  
Christof Teuscher ◽  
Darko Stefanovic
Keyword(s):  
State Of The Art ◽  
Chemical Species ◽  
Mass Action ◽  
Mass Action Kinetics ◽  
Dna Strand Displacement ◽  
Autonomous Adaptation ◽  
Biochemical Systems ◽  
Dna Strand ◽  
Logic Functions ◽  
Application Specific

State-of-the-art biochemical systems for medical applications and chemical computing are application-specific and cannot be reprogrammed or trained once fabricated. The implementation of adaptive biochemical systems that would offer flexibility through programmability and autonomous adaptation faces major challenges because of the large number of required chemical species as well as the timing-sensitive feedback loops required for learning. In this paper, we begin addressing these challenges with a novel chemical perceptron that can solve all 14 linearly separable logic functions. The system performs asymmetric chemical arithmetic, learns through reinforcement and supports both Michaelis–Menten as well as mass-action kinetics. To enable cascading of the chemical perceptrons, we introduce thresholds that amplify the outputs. The simplicity of our model makes an actual wet implementation, in particular by DNA-strand displacement, possible.

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

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.

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