Unification as a complexity measure for logic programming
Journal of Logic Programming
Complexity of finding embeddings in a k-tree
SIAM Journal on Algebraic and Discrete Methods
On generating all maximal independent sets
Information Processing Letters
Many hard examples for resolution
Journal of the ACM (JACM)
Tree clustering for constraint networks (research note)
Artificial Intelligence
The monadic second-order logic of graphs VII: graphs as relational structures
Theoretical Computer Science - Special issue on logic and applications to computer science
Tutte polynomials computable in polynomial time
Discrete Mathematics - Algebraic graph theory; a volume dedicated to Gert Sabidussi
Monadic second-order evaluations on tree-decomposable graphs
Theoretical Computer Science - Special issue on selected papers of the International Workshop on Computing by Graph Transformation, Bordeaux, France, March 21–23, 1991
Handle-rewriting hypergraph grammars
Journal of Computer and System Sciences
CYC: a large-scale investment in knowledge infrastructure
Communications of the ACM
Complexity of generalized satisfiability counting problems
Information and Computation
Splitting formulas for Tutte polynomials
Journal of Combinatorial Theory Series B
Logical description of context-free graph languages
Journal of Computer and System Sciences
All structured programs have small tree width and good register allocation
Information and Computation
Upper bounds to the clique width of graphs
Discrete Applied Mathematics
Colored Tutte polynomials and Kaufman brackets for graphs of bounded tree width
SODA '01 Proceedings of the twelfth annual ACM-SIAM symposium on Discrete algorithms
Discrete Applied Mathematics - Special issue on international workshop of graph-theoretic concepts in computer science WG'98 conference selected papers
Complexity classifications of boolean constraint satisfaction problems
Complexity classifications of boolean constraint satisfaction problems
Computers and Intractability: A Guide to the Theory of NP-Completeness
Computers and Intractability: A Guide to the Theory of NP-Completeness
The Design and Analysis of Computer Algorithms
The Design and Analysis of Computer Algorithms
Satisfiability, Branch-Width and Tseitin Tautologies
FOCS '02 Proceedings of the 43rd Symposium on Foundations of Computer Science
Treewidth: Algorithmoc Techniques and Results
MFCS '97 Proceedings of the 22nd International Symposium on Mathematical Foundations of Computer Science
Polynomial Time Recognition of Clique-Width \le \leq 3 Graphs (Extended Abstract)
LATIN '00 Proceedings of the 4th Latin American Symposium on Theoretical Informatics
Efficient Approximation for Triangulation of Minimum Treewidth
UAI '01 Proceedings of the 17th Conference in Uncertainty in Artificial Intelligence
(De)Composition of Situation Calculus Theories
Proceedings of the Seventeenth National Conference on Artificial Intelligence and Twelfth Conference on Innovative Applications of Artificial Intelligence
Farrell polynomials on graphs of bounded tree width
Advances in Applied Mathematics - Special issue on: Formal power series and algebraic combinatorics in memory of Rodica Simion, 1955-2000
The monadic second-order logic of graphs XIV: uniformly sparse graphs and edge set quantifications
Theoretical Computer Science
The complexity of satisfiability problems
STOC '78 Proceedings of the tenth annual ACM symposium on Theory of computing
Using Cutwidth to Improve Symbolic Simulation and Boolean Satisfiability
HLDVT '01 Proceedings of the Sixth IEEE International High-Level Design Validation and Test Workshop (HLDVT'01)
Tree-width and the monadic quantifier hierarchy
Theoretical Computer Science - Logic and complexity in computer science
Dividing and conquering logic
Fusion in relational structures and the verification of monadic second-order properties
Mathematical Structures in Computer Science
Evaluating the Tutte Polynomial for Graphs of Bounded Tree-Width
Combinatorics, Probability and Computing
Coloured Tutte polynomials and Kauffman brackets for graphs of bounded tree width
Discrete Applied Mathematics - Structural decompositions, width parameters, and graph labelings (DAS 5)
Partition-based logical reasoning for first-order and propositional theories
Artificial Intelligence - Special volume on reformulation
Recognizability, hypergraph operations, and logical types
Information and Computation
Approximating clique-width and branch-width
Journal of Combinatorial Theory Series B
On the colored Tutte polynomial of a graph of bounded treewidth
Discrete Applied Mathematics
Theorem proving with structured theories
IJCAI'01 Proceedings of the 17th international joint conference on Artificial intelligence - Volume 1
Fast Counting with Bounded Treewidth
LPAR '08 Proceedings of the 15th International Conference on Logic for Programming, Artificial Intelligence, and Reasoning
A Most General Edge Elimination Polynomial
Graph-Theoretic Concepts in Computer Science
On the Expressive Power of CNF Formulas of Bounded Tree- and Clique-Width
Graph-Theoretic Concepts in Computer Science
Variable Influences in Conjunctive Normal Forms
SAT '09 Proceedings of the 12th International Conference on Theory and Applications of Satisfiability Testing
An extension of the bivariate chromatic polynomial
European Journal of Combinatorics
Algorithms for propositional model counting
Journal of Discrete Algorithms
Bounded treewidth as a key to tractability of knowledge representation and reasoning
Artificial Intelligence
Bridging the gap between intensional and extensional query evaluation in probabilistic databases
Proceedings of the 13th International Conference on Extending Database Technology
Algorithms for propositional model counting
LPAR'07 Proceedings of the 14th international conference on Logic for programming, artificial intelligence and reasoning
Tree-width in Algebraic Complexity
Fundamenta Informaticae - Bridging Logic and Computer Science: to Johann A. Makowsky for his 60th birthday
On the expressive power of CNF formulas of bounded tree- and clique-width
Discrete Applied Mathematics
Does treewidth help in modal satisfiability?
MFCS'10 Proceedings of the 35th international conference on Mathematical foundations of computer science
Compact labelings for efficient first-order model-checking
Journal of Combinatorial Optimization
The enumeration of vertex induced subgraphs with respect to the number of components
European Journal of Combinatorics
An extended tree-width notion for directed graphs related to the computation of permanents
CSR'11 Proceedings of the 6th international conference on Computer science: theory and applications
F-rank-width of (edge-colored) graphs
CAI'11 Proceedings of the 4th international conference on Algebraic informatics
Satisfiability of acyclic and almost acyclic CNF formulas (II)
SAT'11 Proceedings of the 14th international conference on Theory and application of satisfiability testing
Characterizing arithmetic circuit classes by constraint satisfaction problems
ICALP'11 Proceedings of the 38th international colloquim conference on Automata, languages and programming - Volume Part I
Computing graph polynomials on graphs of bounded clique-width
WG'06 Proceedings of the 32nd international conference on Graph-Theoretic Concepts in Computer Science
Solving #SAT using vertex covers
SAT'06 Proceedings of the 9th international conference on Theory and Applications of Satisfiability Testing
Efficient arbitrary and resolution proofs of unsatisfiability for restricted tree-width
LATIN'12 Proceedings of the 10th Latin American international conference on Theoretical Informatics
On the tractability of query compilation and bounded treewidth
Proceedings of the 15th International Conference on Database Theory
Some remarks on the incompressibility of width-parameterized SAT instances
FAW-AAIM'12 Proceedings of the 6th international Frontiers in Algorithmics, and Proceedings of the 8th international conference on Algorithmic Aspects in Information and Management
The Multivariate Algorithmic Revolution and Beyond
Strong backdoors to nested satisfiability
SAT'12 Proceedings of the 15th international conference on Theory and Applications of Satisfiability Testing
ICALP'12 Proceedings of the 39th international colloquium conference on Automata, Languages, and Programming - Volume Part I
Satisfiability of acyclic and almost acyclic CNF formulas
Theoretical Computer Science
Does Treewidth Help in Modal Satisfiability?
ACM Transactions on Computational Logic (TOCL)
The complexity of weighted counting for acyclic conjunctive queries
Journal of Computer and System Sciences
Better Algorithms for Satisfiability Problems for Formulas of Bounded Rank-width
Fundamenta Informaticae - MFCS & CSL 2010 Satellite Workshops: Selected Papers
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We study algorithms for @?SAT and its generalized version @?GENSAT, the problem of computing the number of satisfying assignments of a set of propositional clauses @S. For this purpose we consider the clauses given by their incidence graph, a signed bipartite graph SI(@S), and its derived graphs I(@S) and P(@S). It is well known, that, given a graph of tree-width k, a k-tree decomposition can be found in polynomial time. Very recently Oum and Seymour have shown that, given a graph of clique-width k, a (2^3^k^+^2-1)-parse tree witnessing clique-width can be found in polynomial time. In this paper we present an algorithm for @?GENSAT for formulas of bounded tree-width k which runs in time 4^k(n+n^2.log"2(n)), where n is the size of the input. The main ingredient of the algorithm is a splitting formula for the number of satisfying assignments for a set of clauses @S where the incidence graph I(@S) is a union of two graphs G"1 and G"2 with a shared induced subgraph H of size at most k. We also present analogue improvements for algorithms for formulas of bounded clique-width which are given together with their derivation. This considerably improves results for @?SAT, and hence also for SAT, previously obtained by Courcelle et al. [On the fixed parameter complexity of graph enumeration problems definable in monadic second order logic, Discrete Appl. Math. 108 (1-2) (2001) 23-52].