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

Theorems of Pappus and Guldinus: Problem Solving01:12

Theorems of Pappus and Guldinus: Problem Solving

Pappus and Guldinus's theorems are powerful mathematical principles that are used for finding the surface area and volume of composite shapes. For example, consider a cylindrical storage tank with a conical top. Finding the surface area or volume can be challenging for such complex shapes. These theorems are particularly useful in calculating the volume and surface area of such systems. Here, the cylindrical storage tank with a conical top can be broken down into two simple shapes: a cylinder...
Theorems of Pappus and Guldinus01:10

Theorems of Pappus and Guldinus

The two theorems developed by Pappus and Guldinus are widely used in mathematics, engineering, and physics to find the surface area and volume of any body of revolution. This is done by revolving a plane curve around an axis that does not intersect the curve to find its surface area or revolving a plane area around a non-intersecting axis to calculate its volume.
For finding the surface area, consider a differential line element that generates a ring with surface area dA when revolved.
Deductive Reasoning01:16

Deductive Reasoning

Deductive reasoning, or deduction, is the type of logic used in hypothesis-based science. In deductive reasoning, the pattern of thinking moves in the opposite direction from inductive reasoning. It uses a general principle or law to predict specific results. From these general principles, a scientist can predict specific results that remain valid as long as the general principles are correct.For example, a researcher can make specific predictions from the hypothesis "butterflies are attracted...
Extended Versions of Green’s Theorem01:27

Extended Versions of Green’s Theorem

Green’s Theorem connects the circulation of a vector field around a closed curve with the behavior of the field across the region enclosed by that curve. It provides a way to replace a line integral around a boundary with a double integral over the interior region, making it especially useful in plane geometry, fluid flow, and vector calculus.Although Green’s Theorem is often introduced using simple regions without gaps, it can also be applied to regions made from several simple parts. This...
Block Diagram Reduction01:22

Block Diagram Reduction

The process of deriving the transfer function of a control system often involves reducing its block diagram to a single block. This simplification can be achieved through a series of strategic operations, including relocating branch points and comparators. These operations preserve the overall function of the system while allowing for easier manipulation and combination of blocks.
The first step in this process is the identification and relocation of a branch point. A branch point, where a...
Fundamental Theorem of Algebra01:30

Fundamental Theorem of Algebra

The Fundamental Theorem of Algebra is central to the study of polynomial equations, asserting that every non-constant polynomial with complex coefficients has at least one complex zero. This means that a polynomial of degree n ≥ 1, written as:  with an ≠ 0, has at least one solution in the complex number system. Since the set of real numbers is a subset of complex numbers, this theorem applies equally to polynomials with real coefficients.Building on this result, the Complete Factorization...

You might also read

Related Articles

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

Sort by
Same journal

Reoptimization of parameterized problems.

Acta informatica·2022
Same journal

Indecision and delays are the parents of failure-taming them algorithmically by synthesizing delay-resilient control.

Acta informatica·2021
Same journal

Automated formal synthesis of provably safe digital controllers for continuous plants.

Acta informatica·2020
Same journal

Synthesis from hyperproperties.

Acta informatica·2020
Same journal

Performance heuristics for GR(1) synthesis and related algorithms.

Acta informatica·2020
Same journal

Characteristic bisimulation for higher-order session processes.

Acta informatica·2020
See all related articles

Related Experiment Videos

A natural deduction system for the Byzantine Generals Oral Messages algorithm.

Dennis M Volpano1

  • 1National Institute of Aerospace, 1100 Exploration Way, Hampton, VA 23666 USA.

Acta Informatica
|June 19, 2026
PubMed
Summary
This summary is machine-generated.

The Oral Messages algorithm (OM(m)) solves the Byzantine Generals Problem using m message rounds. This study clarifies its informal proof with a new natural deduction system, enhancing understanding of its success and limitations.

Related Experiment Videos

Area of Science:

  • Computer Science
  • Distributed Computing
  • Algorithm Analysis

Background:

  • The Byzantine Generals Problem is a fundamental challenge in distributed computing.
  • The Oral Messages algorithm (OM(m)) is a key solution but lacks a clear formal proof.
  • Existing specifications and proofs are difficult to understand, hindering practical application.

Purpose of the Study:

  • To provide a formal and understandable correctness proof for the Oral Messages algorithm (OM(m)).
  • To clarify the role of the parameter 'm' (message relay rounds) in the algorithm's success.
  • To analyze the inherent risks and constraints of the OM(m) algorithm.

Main Methods:

  • Formulating a natural deduction system directly from the OM(m) algorithm's message flows.
  • Utilizing only two inference rules within the natural deduction system.
  • Developing derivations to explain the OM(m) algorithm and its correctness.

Main Results:

  • The natural deduction system successfully explains the OM(m) algorithm.
  • The system's completeness relative to OM(m) is proven.
  • The soundness of the system is demonstrated, preventing impossible consensus derivations.

Conclusions:

  • The formalized proof enhances understanding of OM(m)'s mechanics and correctness.
  • The study clarifies why OM(m) succeeds under specific, well-known constraints.
  • This work provides a rigorous foundation for the OM(m) algorithm in solving the Byzantine Generals Problem.