Maximum satisfiability (MaxSAT) is today a competitive approach to tackling NP-hard optimization problems in a variety of AI and industrial domains. A great majority of the modern state-of-the-art MaxSAT solvers are core-guided, relying on a SAT solver to iteratively extract unsatisfiable cores of the soft clauses in the working formula and ruling out the found cores via adding cardinality cons...

In this paper, we present the complete classification of recursive relationships and the criteria that contribute to the structural validity of modeling recursive relationships within the entity-relationship (ER) diagram. Unlike typical other analyses that use only maximum cardinality constraints, we have used both maximum and minimum cardinality constraints in defining the properties and their...

Constraint query languages with Boolean algebra linear cardinality constraints were introduced recently and shown to be evaluable using a quantifier elimination method in [22]. However, the expressive power of constraint query languages with linear cardinality constraints is still poorly understood in comparison with other cases of constraint query languages. This paper makes several contributi...

Typestate systems ensure many desirable properties of imperative programs, including initialization of object fields and correct use of stateful library interfaces. Abstract sets with cardinality constraints naturally generalize typestate properties: relationships between the typestates of objects can be expressed as subset and disjointness relations on sets, and elements of sets can be represe...

This paper considers optimization problems with cardinality constraints. Based on a recently introduced reformulation of this problem as a nonlinear program with continuous variables, we first define some problem-tailored constraint qualifications and then show how these constraint qualifications can be used to obtain suitable optimality conditions for cardinality constrained problems. Here, th...

This paper introduce a novel method for maintaining consistency of cardinality constraints in context of dynamic constraint satisfaction. The presented method adopt sensitivity analysis for feasible and minimum cost flows underlying all cardinality constraints. Moreover, we extend a dynamic all-pairs shortest path algorithm to support weight changes, insertion and deletion of multiple edges and...

The symmetric cardinality constraint is described in terms of a set of variables X = {x1, . . . , xk}, which take their values as subsets of V = {v1, . . . , vn}. It constraints the cardinality of the set assigned to each variable to be in an interval [lxi , uxi ] and at the same time it restricts the number of occurrences of each value vj ∈ V in the sets assigned to variables in X to be in an ...

Optimization problems with cardinality constraints are very difficult mathematical programs which are typically solved by global techniques from discrete optimization. Here we introduce a mixed-integer formulation whose standard relaxation still has the same solutions (in the sense of global minima) as the underlying cardinality-constrained problem; the relation between the local minima is also...

We consider the problem of cardinality penalized optimization of a convex function over the probability simplex with additional convex constraints. The classical `1 regularizer fails to promote sparsity on the probability simplex since `1 norm on the probability simplex is trivially constant. We propose a direct relaxation of the minimum cardinality problem and show that it can be efficiently s...

We introduce soft cardinality constraints which need to be satisfied on average only, and thus permit violations in a controlled manner. Starting from a highly expressive but intractable class, we establish a fragment that is maximal with respect to both expressivity and efficiency. More precisely, we characterise the associated implication problem axiomatically and develop a low-degree polynom...