# A Combinatorial Characterization of ResolutionWidth.

### Full-text

Víctor Dalmau, Dec 11, 2014 Available from:-
- "The notion of k-consistency has proven to be very robust and, besides being one of the central concepts in theory of constraint-satisfaction problems, has also emerged independently in areas as diverse as finite model theory [18], graph theory [16], and proof complexity [1]. "

##### Chapter: On the Power of k -Consistency

[Show abstract] [Hide abstract]

**ABSTRACT:**The k-consistency algorithm for constraint-satisfaction problems proceeds, roughly, by finding all partial solutions on at most k variables and iteratively deleting those that cannot be extended to a partial solution by one more variable. It is known that if the core of the structure encoding the scopes of the constraints has treewidth at most k, then the k-consistency algorithm is always correct. We prove the exact converse to this: if the core of the structure encoding the scopes of the constraints does not have treewidth at most k, then the k-consistency algorithm is not always correct. This characterizes the exact power of the k-consistency algorithm in structural terms.08/2007: pages 279-290; - [Show abstract] [Hide abstract]

**ABSTRACT:**This project approaches the study, theoretical development, implementation, and em- pirical validation of formal concepts and the criteria for its use in the construction of predictive and descriptive models for symbolic sequences. In particular we will study the following model types: compression mechanisms (flnite- state compressors and Lempel-Ziv algorithms), generalizations of graphs (probabilistic extensions, decision trees, integration of decision trees with Markov hidden models), gram- matical models (such as categorial grammars), time series, study of subsequences (discov- ery of episodes, frequent sets and association rules; learning of patterns of behaviour). The empirical validation of models will be done through great amounts of real data: university students, oncological data from the Hospital Cl¶‡nico Universitario, biological sequences, climatology data. -
##### Conference Paper: Constraint Propagation as a Proof System.

[Show abstract] [Hide abstract]

**ABSTRACT:**Refutation proofs can be viewed as a special case of constraint propa- gation, which is a fundamental technique in solving constraint-satisfaction prob- lems. The generalization lifts, in a uniform way, the concept of refutation from Boolean satisfiability problems to general constraint-satisfaction problems. On the one hand, this enables us to study and characterize basic concepts, such as refutation width, using tools from finite-model theory. On the other hand, this enables us to introduce new proof systems, based on representation classes, that have not been considered up to this point. We consider ordered binary decision diagrams (OBDDs) as a case study of a representation class for refutations, and compare their strength to well-known proof systems, such as resolution, the Gaus- sian calculus, cutting planes, and Frege systems of bounded alternation-depth. In particular, we show that refutations by ODBBs polynomially simulate resolution and can be exponentially stronger.Principles and Practice of Constraint Programming - CP 2004, 10th International Conference, CP 2004, Toronto, Canada, September 27 - October 1, 2004, Proceedings; 01/2004