Leonid A. Levin: Difference between revisions

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


Main Research Question: How can taxes be simplified and made more efficient without causing distortions in the market?
Research Question: Can random instances of a graph coloring problem be hard on average?


Methodology: The study proposes an innovative tax system called the Equity Tax. This system is designed to replace corporate, dividend, and capital gains taxes. It is applicable to publicly held corporations and works by reflecting the expected true annual return on investments, as perceived by investors, not as defined by law. 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 pre-tax profits since this is what taxpayers maximize. The wealth shelter is paid for by efficiency, not by lost tax. The total capital absorbed by the 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 is a simple, efficient, and cost-effective tax system that avoids the problems associated with other tax systems. It reduces compliance costs, eliminates loopholes, and allows businesses to make tax-neutral decisions. This study suggests that the Equity Tax could be a viable alternative to existing tax systems.
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/0012013v18
Link to Article: https://arxiv.org/abs/0112001v9
Authors:  
Authors:  
arXiv ID: 0012013v18
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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