On the Computation of Local Interchangeability in Soft Constraint Satisfaction Problems

Freuder in (1991) de?ned interchangeability for classical Constraint Satisfaction Problems (CSPs). Recently (2002), we extended the de?nition of interchangeability to Soft CSPs and we introduced two notions of relaxations based on degradation ? and on threshold ? (?neighborhood interchangeability (?NI )and ?neighborhood interchangeability ?NI ). In this paper we study the presence of these relaxed version of interchangeability in random soft CSPs. We give a description of the implementation we used to compute interchangeabilities and to make the tests. The experiments show that there is high occurrence of ?NI and ?NI interchangeability around optimal solution in Fuzzy CSP and weighted CSPs. Thus, these algorithms can be used succesfully in solution update applications. Moreover, it is also showed that NI interchangeability can well approximate full interchangeability (FI )

Symmetry Breaking Using Value Precedence

We present a comprehensive study of the use of value precedence constraints to break value symmetry. We first give a simple encoding of value precedence into ternary constraints that is both efficient and effective at breaking symmetry. We then extend value precedence to deal with a number of generalizations like wreath value and partial interchangeability. We also show that value precedence is closely related to lexicographical ordering. Finally, we consider the interaction between value precedence and symmetry breaking constraints for variable symmetries.Comment: 17th European Conference on Artificial Intelligenc

Central limit theorem for a class of globally correlated random variables

The standard central limit theorem with a Gaussian attractor for the sum of independent random variables may lose its validity in presence of strong correlations between the added random contributions. Here, we study this problem for similar interchangeable globally correlated random variables. Under these conditions, a hierarchical set of equations is derived for the conditional transition probabilities. This result allows us to define different classes of memory mechanisms that depend on a symmetric way on all involved variables. Depending on the correlation mechanisms and single statistics, the corresponding sums are characterized by distinct statistical probability densities. For a class of urn models it is also possible to characterize their domain of attraction which, as in the standard case, is parametrized by the probability density of each random variable. Symmetric and asymmetric $q$-Gaussian attractors $(q<1)$ are a particular case of these models.Comment: 11 pages, 7 figures, Appendixes 5 page

Experimental Evaluation of Interchangeability in Soft CSPs

In [8], Freuder defined interchangeability for classical Constraint Satisfaction Problems (CSPs). Recently [2], we extended the definition of interchangeability to Soft CSPs and we introduced two notions of relaxation based on degradation # and on threshold # ( neighborhood interchangeability ( NI )and # neighborhood interchangeability (#NI )). In this pae