Leonid A. Levin: Difference between revisions

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Title: Leonid A. Levin
Title: Leonid A. Levin


Main Research Question: How can the equity tax and shelter mechanism help solve the problems associated with corporate, dividend, and capital gains taxes?
Research Question: Can random instances of a graph coloring problem be hard on average?


Methodology: The study proposes a simple market mechanism called the Equity Tax. It works for publicly held corporations and aims to solve the issues related to corporate, dividend, and capital gains taxes. The mechanism involves converting the taxes into an annual percentage of stock per year, which is auctioned promptly. The system has no loopholes, requires little regulation, and leaves all business decisions tax-neutral.
Methodology: The researchers used a random graph problem and introduced randomizing reductions to show the intractability of random instances of a graph coloring problem.


Results: The Equity Tax enlarges the pre-tax profit since this is what the taxpayers maximize, not a different after-tax net. The wealth shelter is paid for by efficiency, not by lost tax. The total capital absorbed by the equity-taxed sector is the only thing the tax could possibly distort. The rates should be matched to minimize this distortion.
Results: The researchers proved that the graph problem is hard on average unless all NP problems under all samplable distributions are easy. This poses significant technical difficulties.


Implications: The Equity Tax mechanism offers a solution to the problems associated with corporate, dividend, and capital gains taxes. It avoids the major costs of taxes, such as deadweight from distorted incentives and compliance costs. Furthermore, it reduces the revenue-neutral tax rate and requires less regulation, making it a promising approach for tax reform.
Implications: This work provides a strong hardness result related to "typical" or "average" instances of a problem, which is crucial for understanding the efficiency of algorithms and the P=NP question. It also shows that average case completeness of a random graph problem is unlikely without introducing randomizing reductions.


Link to Article: https://arxiv.org/abs/0012013v16
Link to Article: https://arxiv.org/abs/0112001v9
Authors:  
Authors:  
arXiv ID: 0012013v16
arXiv ID: 0112001v9


[[Category:Computer Science]]
[[Category:Computer Science]]
[[Category:Problem]]
[[Category:Graph]]
[[Category:Random]]
[[Category:Average]]
[[Category:Instances]]

Latest revision as of 03:43, 24 December 2023

Title: Leonid A. Levin

Research Question: Can random instances of a graph coloring problem be hard on average?

Methodology: The researchers used a random graph problem and introduced randomizing reductions to show the intractability of random instances of a graph coloring problem.

Results: The researchers proved that the graph problem is hard on average unless all NP problems under all samplable distributions are easy. This poses significant technical difficulties.

Implications: This work provides a strong hardness result related to "typical" or "average" instances of a problem, which is crucial for understanding the efficiency of algorithms and the P=NP question. It also shows that average case completeness of a random graph problem is unlikely without introducing randomizing reductions.

Link to Article: https://arxiv.org/abs/0112001v9 Authors: arXiv ID: 0112001v9

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