Backmarking

	Backmarking In 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 ..., backmarking is a variant of the backtracking algorithm. Backmarking works like backtracking by iteratively evaluating variables in a given order, for example, x_1,\ldots,x_n. It improves over backtracking by maintaining information about the last time a variable x_i was instantiated to a value and information about what changed since then. In particular: # for each variable x_i and value a, the algorithm records information about the last time x_i has been set to a; in particular, it stores the minimal index j such that the assignment to $x_1,\ldots,x_j,x_i$ was then inconsistent; # for each vari ... [...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]
picture info	Backtracking Backtracking is a class of algorithms for finding solutions to some computational problems, notably constraint satisfaction problems, that incrementally builds candidates to the solutions, and abandons a candidate ("backtracks") as soon as it determines that the candidate cannot possibly be completed to a valid solution. The classic textbook example of the use of backtracking is the eight queens puzzle, that asks for all arrangements of eight chess queens on a standard chessboard so that no queen attacks any other. In the common backtracking approach, the partial candidates are arrangements of ''k'' queens in the first ''k'' rows of the board, all in different rows and columns. Any partial solution that contains two mutually attacking queens can be abandoned. Backtracking can be applied only for problems which admit the concept of a "partial candidate solution" and a relatively quick test of whether it can possibly be completed to a valid solution. It is useless, for example ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu]
	Inconsistent In classical deductive logic, a consistent theory is one that does not lead to a logical contradiction. The lack of contradiction can be defined in either semantic or syntactic terms. The semantic definition states that a theory is consistent if it has a model, i.e., there exists an interpretation under which all formulas in the theory are true. This is the sense used in traditional Aristotelian logic, although in contemporary mathematical logic the term ''satisfiable'' is used instead. The syntactic definition states a theory T is consistent if there is no formula \varphi such that both \varphi and its negation \lnot\varphi are elements of the set of consequences of T. Let A be a set of closed sentences (informally "axioms") and \langle A\rangle the set of closed sentences provable from A under some (specified, possibly implicitly) formal deductive system. The set of axioms A is consistent when \varphi, \lnot \varphi \in \langle A \rangle for no formula \varphi. If there exis ... [...More Info...] [...Related Items...] OR: [Wikipedia] [Google] [Baidu]