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Notice that the actual constraint graph representing this problem must contain two edges between X and Y since C2 is undirected but the graph representation being used by AC-3 is directed. AC-3 solves the problem by first removing the non-even values from of the domain of X as required by C1, leaving D(X) = { 0, 2, 4 }. It then examines the ...
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 unbounded variant was shown to be NP-complete in 1975 by Lueker. [3] Both the bounded and unbounded variants admit an FPTAS (essentially the same as the one used in the 0-1 knapsack problem). If the items are subdivided into k classes denoted N i {\displaystyle N_{i}} , and exactly one item must be taken from each class, we get the multiple ...
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 ...
Boolean logic allows 2 2 = 4 unary operators; the addition of a third value in ternary logic leads to a total of 3 3 = 27 distinct operators on a single input value. (This may be made clear by considering all possible truth tables for an arbitrary unary operator.
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.
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In logic, linear temporal logic or linear-time temporal logic [1] [2] (LTL) is a modal temporal logic with modalities referring to time. In LTL, one can encode formulae about the future of paths, e.g., a condition will eventually be true, a condition will be true until another fact becomes true, etc.