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Set constraints obtained from abstract interpretation of the Collatz algorithm. In mathematics and theoretical computer science, a set constraint is an equation or an inequation between sets of terms. Similar to systems of equations between numbers, methods are studied for
The second and third lines define two constraints, the first of which is an inequality constraint and the second of which is an equality constraint. These two constraints are hard constraints, meaning that it is required that they be satisfied; they define the feasible set of candidate solutions.
Constraint satisfaction problems (CSPs) are mathematical questions defined as a set of objects whose state must satisfy a number of constraints or limitations.CSPs represent the entities in a problem as a homogeneous collection of finite constraints over variables, which is solved by constraint satisfaction methods.
The constraints in the goal and in the clauses used to prove the goal are accumulated into a set called constraint store. This set contains the constraints the interpreter has assumed satisfiable in order to proceed in the evaluation. As a result, if this set is detected unsatisfiable, the interpreter backtracks.
Constraints can be either hard constraints, which set conditions for the variables that are required to be satisfied, or soft constraints, which have some variable values that are penalized in the objective function if, and based on the extent that, the conditions on the variables are not satisfied.
Two constraints are relational path consistent with a variable if every consistent assignment to all their variables but the considered one can be extended in such a way the two constraints are satisfied. For more than two constraints, relational -consistency is defined. Relational -consistency involves a set of constraints and a variable that ...
This article lists mathematical properties and laws of sets, involving the set-theoretic operations of union, intersection, and complementation and the relations of set equality and set inclusion. It also provides systematic procedures for evaluating expressions, and performing calculations, involving these operations and relations.
A hinge decomposition of a constraint satisfaction problem is a tree whose nodes are some minimal hinges of the hypergraph associated to the problem and such that some other conditions are met. By the correspondence of problems with hypergraphs, a hinge is a set of scopes of constraints, and can therefore be considered as a set of constraints.