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Graph rewriting: an algebraic and logic approach
Handbook of theoretical computer science (vol. B)
A Linear-Time Algorithm for Finding Tree-Decompositions of Small Treewidth
SIAM Journal on Computing
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Journal of the ACM (JACM)
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CSL '99 Proceedings of the 13th International Workshop and 8th Annual Conference of the EACSL on Computer Science Logic
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Theoretical Computer Science - Mathematical foundations of computer science 2000
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Proceedings of the twenty-sixth ACM SIGMOD-SIGACT-SIGART symposium on Principles of database systems
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Discrete Applied Mathematics
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AAAI'06 Proceedings of the 21st national conference on Artificial intelligence - Volume 1
Abduction with bounded treewidth: from theoretical tractability to practically efficient computation
AAAI'08 Proceedings of the 23rd national conference on Artificial intelligence - Volume 3
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IJCAI'07 Proceedings of the 20th international joint conference on Artifical intelligence
The first answer set programming system competition
LPNMR'07 Proceedings of the 9th international conference on Logic programming and nonmonotonic reasoning
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LPAR'07 Proceedings of the 14th international conference on Logic for programming, artificial intelligence and reasoning
Counting and enumeration problems with bounded treewidth
LPAR'10 Proceedings of the 16th international conference on Logic for programming, artificial intelligence, and reasoning
Gaussian logic for predictive classification
ECML PKDD'11 Proceedings of the 2011 European conference on Machine learning and knowledge discovery in databases - Volume Part II
The Complexity of Reasoning for Fragments of Autoepistemic Logic
ACM Transactions on Computational Logic (TOCL)
Exploiting bounded treewidth with datalog (a survey)
Datalog'10 Proceedings of the First international conference on Datalog Reloaded
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Many intractable problems have been shown to become tractable if the treewidth of the underlying structure is bounded by a constant. An important tool for deriving such results is Courcelle's Theorem, which states that all properties defined by Monadic-Second Order (MSO) sentences are fixed-parameter tractable with respect to the treewidth. Arnborg et al. extended this result to counting problems defined via MSO properties. However, the MSO description of a problem is of course not an algorithm. Consequently, proving the fixed-parameter tractability of some problem via Courcelle's Theorem can be considered as the starting point rather than the endpoint of the search for an efficient algorithm. Gottlob et al. have recently presented a new approach via monadic datalog to actually devise efficient algorithms for decision problems whose tractability follows from Courcelle's Theorem. In this paper, we extend this approach and apply it to some fundamental counting problems in logic an artificial intelligence.