Jove
Visualize
Contact Us
JoVE
x logofacebook logolinkedin logoyoutube logo
ABOUT JoVE
OverviewLeadershipBlogJoVE Help Center
AUTHORS
Publishing ProcessEditorial BoardScope & PoliciesPeer ReviewFAQSubmit
LIBRARIANS
TestimonialsSubscriptionsAccessResourcesLibrary Advisory BoardFAQ
RESEARCH
JoVE JournalMethods CollectionsJoVE Encyclopedia of ExperimentsArchive
EDUCATION
JoVE CoreJoVE BusinessJoVE Science EducationJoVE Lab ManualFaculty Resource CenterFaculty Site
Terms & Conditions of Use
Privacy Policy
Policies

Related Concept Videos

Sum and Difference OpAmps01:22

Sum and Difference OpAmps

1.5K
Operational amplifiers (op-amps) are versatile devices that extend beyond amplification. In this context, two specific op-amp configurations are explored: the summing and difference amplifiers.
A summing amplifier, or an adder, utilizes an op-amp to merge multiple input signals into a single output signal. When audio signals are introduced into its input channels, the input resistors initiate currents that traverse feedback resistors, resulting in an output voltage. Applying Kirchhoff's current...
1.5K
First-Order Circuits01:15

First-Order Circuits

4.9K
First-order electrical circuits, which comprise resistors and a single energy storage element - either a capacitor or an inductor, are fundamental to many electronic systems. These circuits are governed by a first-order differential equation that describes the relationship between input and output signals.
One common example of a first-order circuit is the RC (resistor-capacitor) circuit. These circuits are used in relaxation oscillators such as neon lamp oscillator circuits. When voltage is...
4.9K
Second-Order Circuits01:17

Second-Order Circuits

3.8K
Integrating two fundamental energy storage elements in electrical circuits results in second-order circuits, encompassing RLC circuits and circuits with dual capacitors or inductors (RC and RL circuits). Second-order circuits are identified by second-order differential equations that link input and output signals.
Input signals typically originate from voltage or current sources, with the output often representing voltage across the capacitor and/or current through the inductor. For example, in...
3.8K
Even and Odd Signals01:17

Even and Odd Signals

2.3K
An even signal, whether in continuous-time or discrete-time, is defined by its symmetry with its time-reversed version. Mathematically, this is represented as
2.3K
Superposition Theorem for AC Circuits01:13

Superposition Theorem for AC Circuits

1.9K
Consider encountering a circuit in a steady state where all its inputs are sinusoidal, yet they do not all possess the same frequency. Such a circuit is not classified as an alternating current (AC) circuit, and consequently, its currents and voltages will not exhibit sinusoidal behavior. However, this circuit can be analyzed using the principle of superposition.
The principle of superposition stipulates that the output of a linear circuit with several concurrent inputs is equivalent to the...
1.9K
Norton Equivalent Circuits01:16

Norton Equivalent Circuits

844
Norton's theorem is a fundamental concept in the field of electrical engineering that allows for the simplification of complex AC circuits. The theorem states that any two-terminal linear network can be replaced with an equivalent circuit that consists of an impedance, which is parallel with a constant current source. Figure 1 shows the AC circuit portioned into two parts: Circuit A and Circuit B, while Figure 2 depicts the circuit obtained by replacing Circuit A by its Norton equivalent...
844

You might also read

Related Articles

Articles linked to this work by shared authors, journal, and citation graph.

Sort by
Same author

Heterogeneity in the association between social support and mental distress in old-age retirees - a computational approach using longitudinal cohort data.

BMC geriatrics·2024
Same author

Explicit Correlation Amplifiers for Finding Outlier Correlations in Deterministic Subquadratic Time.

Algorithmica·2020
Same author

A Constraint Optimization Approach to Causal Discovery from Subsampled Time Series Data.

International journal of approximate reasoning : official publication of the North American Fuzzy Information Processing Society·2018
Same author

Causal Discovery from Subsampled Time Series Data by Constraint Optimization.

JMLR workshop and conference proceedings·2017
Same author

Fast motif matching revisited: high-order PWMs, SNPs and indels.

Bioinformatics (Oxford, England)·2016
Same author

Mixture model clustering of phenotype features reveals evidence for association of DTNBP1 to a specific subtype of schizophrenia.

Biological psychiatry·2009
Same journal

Rigorously modeling self-stabilizing fault-tolerant circuits: An ultra-robust clocking scheme for systems-on-chip.

Journal of computer and system sciences·2015
Same journal

Strategy improvement for concurrent reachability and turn-based stochastic safety games.

Journal of computer and system sciences·2015
See all related articles

Related Experiment Video

Updated: Mar 2, 2026

Gene Digital Circuits Based on CRISPR-Cas Systems and Anti-CRISPR Proteins
10:46

Gene Digital Circuits Based on CRISPR-Cas Systems and Anti-CRISPR Proteins

Published on: October 18, 2022

2.3K

Separating OR, SUM, and XOR Circuits.

Magnus Find1, Mika Göös2,3, Matti Järvisalo3

  • 1National Institute of Standards and Technology, USA.

Journal of Computer and System Sciences
|May 23, 2017
PubMed
Summary
This summary is machine-generated.

Boolean matrix transformations are analyzed using three circuit models: OR, SUM, and XOR. Researchers demonstrate OR-circuits can be significantly more efficient than SUM-circuits for certain matrix computations.

Keywords:
arithmetic circuitsboolean arithmeticidempotent arithmeticmonotone separationsrewriting

More Related Videos

Silicon Metal-oxide-semiconductor Quantum Dots for Single-electron Pumping
14:58

Silicon Metal-oxide-semiconductor Quantum Dots for Single-electron Pumping

Published on: June 3, 2015

15.5K
On-chip Isotachophoresis for Separation of Ions and Purification of Nucleic Acids
10:32

On-chip Isotachophoresis for Separation of Ions and Purification of Nucleic Acids

Published on: March 2, 2012

25.2K

Related Experiment Videos

Last Updated: Mar 2, 2026

Gene Digital Circuits Based on CRISPR-Cas Systems and Anti-CRISPR Proteins
10:46

Gene Digital Circuits Based on CRISPR-Cas Systems and Anti-CRISPR Proteins

Published on: October 18, 2022

2.3K
Silicon Metal-oxide-semiconductor Quantum Dots for Single-electron Pumping
14:58

Silicon Metal-oxide-semiconductor Quantum Dots for Single-electron Pumping

Published on: June 3, 2015

15.5K
On-chip Isotachophoresis for Separation of Ions and Purification of Nucleic Acids
10:32

On-chip Isotachophoresis for Separation of Ions and Purification of Nucleic Acids

Published on: March 2, 2012

25.2K

Area of Science:

  • Theoretical Computer Science
  • Computational Complexity Theory
  • Circuit Complexity

Background:

  • Boolean matrices and linear transformations are fundamental in computer science.
  • Arithmetic circuits provide a model for computation with varying complexity measures.
  • Understanding the relative power of different circuit models is crucial for algorithm design.

Purpose of the Study:

  • To compare the circuit complexity of computing matrix-vector multiplication (x ↦ Ax) across different semiring models.
  • To investigate the separation in computational power between monotone OR-circuits and SUM/XOR-circuits.
  • To analyze the complexity of converting OR-circuits to XOR-circuits.

Main Methods:

  • Analysis of arithmetic circuit models: monotone OR-circuits, monotone SUM-circuits, and non-monotone XOR-circuits.
  • Derivation of lower bounds for SUM-circuit complexity based on matrix properties.
  • Exploration of the relationship between OR-circuit size and XOR-circuit conversion time.

Main Results:

  • Matrices exist that are computable by O(n) size OR-circuits but require Ω(n^(3/2)/log^2 n) size SUM-circuits.
  • A subquadratic-time algorithm for rewriting OR-circuits as XOR-circuits would violate the Strong Exponential Time Hypothesis.

Conclusions:

  • Monotone OR-circuits offer a distinct computational advantage over SUM-circuits for specific matrix transformations.
  • Efficiently rewriting OR-circuits into XOR-circuits is computationally hard, with implications for complexity theory.