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Created page with "Title: Paolo Liberatore Main Research Question: How efficient are the popular methods DPLL and resolution for solving the problem of propositional satisfiability, and how hard is it to make the optimal choices during execution? Methodology: The study uses mathematical analysis and computational complexity theory to investigate the efficiency of DPLL and resolution algorithms. It compares the complexity of making optimal choices in these algorithms, such as choosing th..."
 
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Title: Paolo Liberatore
Title: Paolo Liberatore


Main Research Question: How efficient are the popular methods DPLL and resolution for solving the problem of propositional satisfiability, and how hard is it to make the optimal choices during execution?
Main Research Question: Can the computational complexity of abduction be reduced by an appropriate use of preprocessing?


Methodology: The study uses mathematical analysis and computational complexity theory to investigate the efficiency of DPLL and resolution algorithms. It compares the complexity of making optimal choices in these algorithms, such as choosing the best literal to branch on in DPLL or selecting the right pair of clauses to resolve in resolution.
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.


Results: The study proves that choosing the optimal literal to branch on in DPLL is ∆p[logn]-hard and becomes NPPP-hard if branching is only allowed on a subset of variables. Optimal choice in resolution is both NP-hard and coNP-hard. The problem of determining the size of the optimal proofs is also analyzed, and previous hardness results are enhanced.
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.


Implications: These results suggest that making optimal choices in DPLL and resolution can be computationally challenging, potentially leading to increased computational complexity and time. This could have implications for the practical implementation and efficiency of these algorithms. The study also contributes to the ongoing discussion about the automatizability of these methods, providing insights into their potential limitations.
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.


Link to Article: https://arxiv.org/abs/0209032v1
Link to Article: https://arxiv.org/abs/0210007v1
Authors:  
Authors:  
arXiv ID: 0209032v1
arXiv ID: 0210007v1

Revision as of 06:41, 24 December 2023

Title: Paolo Liberatore

Main Research Question: Can the computational complexity of abduction be reduced by an appropriate use of preprocessing?

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.

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.

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.

Link to Article: https://arxiv.org/abs/0210007v1 Authors: arXiv ID: 0210007v1