Many important problems in Artificial Intelligence can be defined as Constraint Satisfaction Problems (CSP). These types of problems are defined by a limited set of variables, each having a limited domain and a number of Constraints on the values of those variables (these problems are also called Consistent Labeling Problems (CLP), in which “Labeling" means assigning a value to a variable.) Sol...

We discuss a method of producing computer assisted proofs of almost everywhere strong convergence of the d-dimensional Gauss algorithm. This algorithm is equivalent to Brun's algorithm and to the modi ed Jacobi-Perron algorithm considered by Podsypanin and Schweiger. In this paper we focus on the reduction of the problem to a nite number of calculations. These calculations have been carried out...

The paper provides a unifying perspective of tree-decomposition algorithms appearing in various automated reasoning areas such as join-tree clustering for constraint-satisfaction and the cliquetree algorithm for probabilistic reasoning. Within this framework, we introduce a new algorithm, called bucket-tree elimination (BTE), that extends Bucket Elimination (BE) to trees, and show that it can p...

Compiling solver-independent constraint models to solver input typically involves flattening, the decomposition of complex expressions into simpler expressions, introducing additional variables and constraints. In previous work [8], we have informally proposed extending flattening problem instances with common subexpression elimination(CSE), a widespread optimisation technique that has not yet ...

When solving a problem using constraint programming, constraint modelling is widely acknowledged as an important and difficult task. Even a constraint modelling expert may explore many models and spend considerable time modelling a single problem. Therefore any automated assistance in the area of constraint modelling is valuable. Common sub-expression elimination (CSE) is a type of constraint r...

When solving a combinatorial problem using Constraint Programming (CP) or Satisfiability (SAT), modelling and formulation are vital and difficult tasks. Even an expert human may explore many alternatives in modelling a single problem. We make a number of contributions in the automated modelling and reformulation of constraint models. We study a range of automated reformulation techniques, findi...

Variable elimination is a general technique for constraint processing. It is often discarded because of its high space complexity. However, it can be extremely useful when combined with other techniques. In this paper we study the applicability of variable elimination to the challenging problem of nding still-lifes. We illustrate several alternatives: variable elimination as a stand-alone algor...

In this paper we will show how constraint solving methods can be applied for the recognition of buildings in aerial images. Object models are transformed to constraint representations which are matched against extracted image features. To cope with disturbances caused by occlusions and noise, we distinguish between the unobservability of a) relations between object parts and b) object parts the...

Systems of Boolean constraints which allow negative constraints such as f 6 6 g are investigated. The results form a basis for algorithms to determine satissability, validity, implication, equivalence and variable elimination for such systems. These algorithms have applications in spatial query decomposition, machine reasoning, and constraint logic programming. Proofs of the results rely on ind...