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Only the pairs (X=0, Y=4), (X=2, Y=2), and (X=4, Y=0) match the constraint C2. AC-3 then terminates, with D(X) = {0, 2, 4} and D(Y) = {0, 2, 4}. AC-3 is expressed in pseudocode as follows: Input: A set of variables X A set of domains D(x) for each variable x in X. D(x) contains vx0, vx1... vxn, the possible values of x A set of unary ...
The AC-3 algorithm improves over this algorithm by ignoring constraints that have not been modified since they were last analyzed. In particular, it works on a set of constraints that initially contains all constraints; at each step, it takes a constraint and enforces arc consistency; if this operation may have produced a violation of arc ...
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 CAP theorem is based on three trade-offs, one of which is "atomic consistency" (shortened to "consistency" for the acronym), about which the authors note, "Discussing atomic consistency is somewhat different than talking about an ACID database, as database consistency refers to transactions, while atomic consistency refers only to a property of a single request/response operation sequence.
Constraints with one, two, or more variables are called unary, binary, or higher-order constraints. The number of variables in a constraint is called its arity. The hidden transformation replaces each constraint with a new, hidden variable. The hidden transformation converts an arbitrary constraint satisfaction problem into a binary one.
In artificial intelligence and operations research, a Weighted Constraint Satisfaction Problem (WCSP), also known as Valued Constraint Satisfaction Problem (VCSP), is a generalization of a constraint satisfaction problem (CSP) where some of the constraints can be violated (according to a violation degree) and in which preferences among solutions can be expressed.
In relational algebra, a selection (sometimes called a restriction in reference to E.F. Codd's 1970 paper [1] and not, contrary to a popular belief, to avoid confusion with SQL's use of SELECT, since Codd's article predates the existence of SQL) is a unary operation that denotes a subset of a relation.
A table in a SQL database schema corresponds to a predicate variable; the contents of a table to a relation; key constraints, other constraints, and SQL queries correspond to predicates. However, SQL databases deviate from the relational model in many details, and Codd fiercely argued against deviations that compromise the original principles. [3]