Search research articles

ABOUT JoVE

Overview Leadership Blog JoVE Help Center

AUTHORS

Publishing Process Editorial Board Scope & Policies Peer Review FAQ Submit

LIBRARIANS

Testimonials Subscriptions Access Resources Library Advisory Board FAQ

RESEARCH

JoVE Journal Methods Collections JoVE Encyclopedia of Experiments Archive

EDUCATION

JoVE Core JoVE Business JoVE Science Education JoVE Lab Manual Faculty Resource Center Faculty Site

Terms & Conditions of Use

Related Concept Videos

Fundamental Theorem of Algebra

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...

Method of Sections: Problem Solving II

Method of Sections: Problem Solving II

Consider an arbitrary truss structure composed of diagonal, vertical, and horizontal members fixed to the wall. To calculate the force acting on members CB, GB, and GH, method of sections can be used. The loads and lengths of the horizontal and vertical members are known parameters, as shown in the figure.

Theorems of Pappus and Guldinus: Problem Solving

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...

Block Diagram Reduction

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...

Method of Sections: Problem Solving I

Method of Sections: Problem Solving I

Consider a symmetrical roof truss structure, composed of vertical, diagonal, and horizontal members. The length of each horizontal member is 4 m. The lengths of the vertical members FB and HD are 4 m, while the length of member GC is 6 m. The loads acting at joints F, G, and H are 2 kN, while those at joints A and E are 1 kN.

SFG Algebra

SFG Algebra

In Signal Flow Graph (SFG) algebra, the value a node represents is determined by the sum of all signals entering that node. This summed value is then transmitted through every branch leaving the node, making the SFG a powerful tool for visualizing and analyzing control systems.
Each node in an SFG corresponds to a variable, and the interactions between nodes are represented by branches with associated gains. When multiple branches lead into a node, the value at that node is the sum of the...

You might also read

Related Articles

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

Sort by

Same author

Proof Complexity of Modal Resolution.

Journal of automated reasoning·2022

Same author

Reinterpreting Dependency Schemes: Soundness Meets Incompleteness in DQBF.

Journal of automated reasoning·2019

Same journal

Combining Higher-Order Logic with Set Theory Formalizations.

Journal of automated reasoning·2023

Same journal

Synthesising Programs with Non-trivial Constants.

Journal of automated reasoning·2023

Same journal

Unifying Splitting.

Journal of automated reasoning·2023

Same journal

First-Order Theory of Rewriting for Linear Variable-Separated Rewrite Systems: Automation, Formalization, Certification.

Journal of automated reasoning·2023

Same journal

A Formalization of SQL with Nulls.

Journal of automated reasoning·2022

Same journal

A Comprehensive Framework for Saturation Theorem Proving.

Journal of automated reasoning·2022

See all related articles

Search research articles

Related Experiment Video

Updated: Nov 20, 2025

A Quantitative Fitness Analysis Workflow

A Quantitative Fitness Analysis Workflow

Published on: August 13, 2012

Building Strategies into QBF Proofs.

Olaf Beyersdorff¹, Joshua Blinkhorn¹, Meena Mahajan²

¹Institut für Informatik, Friedrich-Schiller-Universität Jena, Jena, Germany.

Journal of Automated Reasoning

|January 25, 2021

Summary

This summary is machine-generated.

This study introduces a novel quantified Boolean formulas (QBF) system where strategies are integrated into proofs, enabling efficient extraction and new inference rules. This approach offers advantages in QBF solving and proof complexity, and extends to dependency QBFs (DQBF).

Keywords:

DQBF Proof complexity QBF Resolution

More Related Videos

Large Scale Energy Efficient Sensor Network Routing Using a Quantum Processor Unit

Large Scale Energy Efficient Sensor Network Routing Using a Quantum Processor Unit

Published on: September 8, 2023

Related Experiment Videos

Last Updated: Nov 20, 2025

A Quantitative Fitness Analysis Workflow

A Quantitative Fitness Analysis Workflow

Published on: August 13, 2012

Large Scale Energy Efficient Sensor Network Routing Using a Quantum Processor Unit

Large Scale Energy Efficient Sensor Network Routing Using a Quantum Processor Unit

Published on: September 8, 2023

Area of Science:

Automated Reasoning
Computational Logic
Theoretical Computer Science

Background:

Strategy extraction is crucial for quantified Boolean formulas (QBF) in solving and proof complexity.
Current methods extract strategies algorithmically from existing proofs.
Existing QBF calculi like Q-Resolution have limitations in strategy integration and inference.

Purpose of the Study:

To develop a new QBF system that integrates (partial) strategies directly into proofs.
To enable piecewise construction of strategies through simple derivation operations.
To explore the advantages of this integrated approach for QBF solving and complexity.

Main Methods:

Devised a novel QBF calculus where strategies are built into the proof structure.
Strategies are constructed piecewise via simple operations during the derivation process.
The calculus naturally supports strategy extraction by design.

Main Results:

The new calculus offers semantic clarity, succinct partial strategy representation, and built-in strategy extraction.
Introduced new sound inference steps, disallowed in previous calculi like Q-Resolution.
Demonstrated an exponential separation between the new system and reductionless long-distance resolution.
Extended the approach to dependency QBFs (DQBF), yielding the first sound and complete CDCL-style calculus for DQBF.

Conclusions:

The proposed QBF system enhances strategy extraction and introduces novel inference capabilities.
The integrated strategy approach provides significant advantages over traditional methods.
The extension to DQBF opens new possibilities for CDCL-based DQBF solving.