Artificial Intelligence
Artificial Intelligence
NP is as easy as detecting unique solutions
Theoretical Computer Science
A theory of diagnosis from first principles
Artificial Intelligence
Hard problems for simple default logics
Proceedings of the first international conference on Principles of knowledge representation and reasoning
Tractable default reasoning
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
The Computational Complexity of Truth Maintenance Systems
The Computational Complexity of Truth Maintenance Systems
On Two Problems in the Generation of Program Test Paths
IEEE Transactions on Software Engineering
A knowledge-level account of abduction
IJCAI'89 Proceedings of the 11th international joint conference on Artificial intelligence - Volume 2
Diagnosis with behavioral modes
IJCAI'89 Proceedings of the 11th international joint conference on Artificial intelligence - Volume 2
Computational complexity of hypothesis assembly
IJCAI'87 Proceedings of the 10th international joint conference on Artificial intelligence - Volume 2
What makes propositional abduction tractable
Artificial Intelligence
Counting complexity of propositional abduction
Journal of Computer and System Sciences
A logical study of partial entailment
Journal of Artificial Intelligence Research
On the generation of alternative explanations with implications for belief revision
UAI'91 Proceedings of the Seventh conference on Uncertainty in Artificial Intelligence
IJCAI'13 Proceedings of the Twenty-Third international joint conference on Artificial Intelligence
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Of all the possible ways of computing abductive explanations, the ATMS procedure is one of the most popular. While this procedure is known to run in exponential time in the worst case, the proof actually depends on the existence of queries with an exponential number of answers. But how much of the difficulty stems from having to return these large sets of explanations? Here we explore abduction tasks similar to that of the ATMS, but which return relatively small answers. The main result is that although it is possible to generate some non-trivial explanations quickly, deciding if there is an explanation containing a given hypothesis is NP-hard, as is the task of generating even one explanation expressed in terms of a given set of assumption letters. Thus, the method of simply listing all explanations, as employed by the ATMS, probably cannot be improved upon. An interesting result of our analysis is the discovery of a subtask that is at the core of generating explanations, and is also at the core of generating extensions in Reiter's default logic. Moreover, it is this subtask that accounts for the computational difficulty of both forms of reasoning. This establishes for the first time a strong connection between computing abductive explanations and computing extensions in default logic.