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Title: Paolo Liberatore
Title: Paolo Liberatore


Main Research Question: Can the computational complexity of abduction be reduced by an appropriate use of preprocessing?
Main Research Question: How does the knowledge of a solution to a similar instance affect the complexity of solving a problem when the instance changes?


Methodology: The researchers investigated the complexity and compilability of abduction, a form of reasoning that involves finding the most likely causes for a given effect. They explored different methods, including allowing ordering, using preferences, and implementing prioritization and penalties.
Methodology: The study uses the theory of NP-completeness and compilability, two key concepts in the field of computer science complexity. The authors consider two scenarios: when only a solution of a previous instance is known, and when additional information, found during the search for this solution, is also known.


Results: The study found that the computational complexity of abduction can be reduced when compilation is allowed. This means that the problem can be broken down into smaller, more manageable parts, making it easier to solve. The researchers also found that the complexity results depend on the ordering of the data and the preferences given to the possible explanations.
Results: The authors provide complexity results for various problems, such as satisfiability, planning, and vertex cover. They show that the presence of both constraints and hints (in this case, the solution of a similar instance) can affect the complexity of solving the problem.


Implications: These findings suggest that abduction, a crucial form of reasoning in many practical problems, can be made more efficient by using preprocessing techniques. This could have significant implications for fields such as artificial intelligence, diagnosis, and debugging, where efficient reasoning is essential.
Implications: This research has implications for the field of computer science and problem-solving in general. It highlights the importance of considering both constraints and hints when analyzing the complexity of problems, especially in scenarios where instances may change over time. The findings can help inform the development of more efficient algorithms and problem-solving strategies in various domains.


Link to Article: https://arxiv.org/abs/0210007v1
Link to Article: https://arxiv.org/abs/0402053v1
Authors:  
Authors:  
arXiv ID: 0210007v1
arXiv ID: 0402053v1
 
[[Category:Computer Science]]
[[Category:Complexity]]
[[Category:Solution]]
[[Category:Instance]]
[[Category:Solving]]
[[Category:Problem]]

Latest revision as of 15:27, 24 December 2023

Title: Paolo Liberatore

Main Research Question: How does the knowledge of a solution to a similar instance affect the complexity of solving a problem when the instance changes?

Methodology: The study uses the theory of NP-completeness and compilability, two key concepts in the field of computer science complexity. The authors consider two scenarios: when only a solution of a previous instance is known, and when additional information, found during the search for this solution, is also known.

Results: The authors provide complexity results for various problems, such as satisfiability, planning, and vertex cover. They show that the presence of both constraints and hints (in this case, the solution of a similar instance) can affect the complexity of solving the problem.

Implications: This research has implications for the field of computer science and problem-solving in general. It highlights the importance of considering both constraints and hints when analyzing the complexity of problems, especially in scenarios where instances may change over time. The findings can help inform the development of more efficient algorithms and problem-solving strategies in various domains.

Link to Article: https://arxiv.org/abs/0402053v1 Authors: arXiv ID: 0402053v1

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