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Constraint Inference
In constraint satisfaction, constraint inference is a relationship between constraints and their consequences. A set of constraints D entails a constraint C if every solution to D is also a solution to C. In other words, if V is a valuation of the variables in the scopes of the constraints in D and all constraints in D are satisfied by V, then V also satisfies the constraint C. Some operations on constraints produce a new constraint that is a consequence of them. Constraint composition operates on a pair of binary constraints ((x,y),R) and ((y,z),S) with a common variable. The composition of such two constraints is the constraint ((x,z),Q) that is satisfied by every evaluation of the two non-shared variables for which there exists a value of the shared variable y such that the evaluation of these three variables satisfies the two original constraints ((x,y),R) and ((y,z),S). Constraint projection restricts the effects of a constraint to some of its variables. Given a constraint (t, ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Constraint Satisfaction
In artificial intelligence and operations research, constraint satisfaction is the process of finding a solution through a set of constraints that impose conditions that the variables must satisfy. A solution is therefore a set of values for the variables that satisfies all constraints—that is, a point in the feasible region. The techniques used in constraint satisfaction depend on the kind of constraints being considered. Often used are constraints on a finite domain, to the point that constraint satisfaction problems are typically identified with problems based on constraints on a finite domain. Such problems are usually solved via search, in particular a form of backtracking or local search. Constraint propagation are other methods used on such problems; most of them are incomplete in general, that is, they may solve the problem or prove it unsatisfiable, but not always. Constraint propagation methods are also used in conjunction with search to make a given proble ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Constraint Satisfaction Problem
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. CSPs are the subject of research in both artificial intelligence and operations research, since the regularity in their formulation provides a common basis to analyze and solve problems of many seemingly unrelated families. CSPs often exhibit high complexity, requiring a combination of heuristics and combinatorial search methods to be solved in a reasonable time. Constraint programming (CP) is the field of research that specifically focuses on tackling these kinds of problems. Additionally, Boolean satisfiability problem (SAT), the satisfiability modulo theories (SMT), mixed integer programming (MIP) and answer set programming (ASP) are all fields of research f ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |
Constraint Programming
Constraint programming (CP) is a paradigm for solving combinatorial problems that draws on a wide range of techniques from artificial intelligence, computer science, and operations research. In constraint programming, users declaratively state the Constraint (mathematics), constraints on the feasible solutions for a set of decision variables. Constraints differ from the common Language primitive, primitives of imperative programming languages in that they do not specify a step or sequence of steps to execute, but rather the properties of a solution to be found. In addition to constraints, users also need to specify a method to solve these constraints. This typically draws upon standard methods like chronological backtracking and constraint propagation, but may use customized code like a problem specific branching Heuristic (computer science), heuristic. Constraint programming takes its root from and can be expressed in the form of constraint logic programming, which embeds constra ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu] |