The partial assignment is not always necessary in full to prove that no value of lead to a solution.

A larger constraint whose violating values are more similar to the current partial assignment may be preferred in such cases.

It maintains a partial assignment of the variables.

It is this partial assignment (arguably a more apt term) that often surprises programmers and leads to unintended consequences.

For each value, the consistency of the partial assignment with the constraints is checked; in case of consistency, a recursive call is performed.

Roof duality may also provide a partial assignment of the variables, indicating some of the values of a minimizer to the polynomial.

The Court of Appeals reasoned the contingent-fee arrangement "is more like a partial assignment of income-producing property than an assignment of income."

More precisely, relational consistency implies that every consistent partial assignment can be extended in such a way that a given constraint or set of constraints is satisfied.

Whenever a partial assignment is found inconsistent, this algorithm selects the violated constraint that is minimal according to an ordering based on the order of instantiation of variables.

Unsatisfiability of a given partial assignment is detected if one clause becomes empty, i.e. if all its variables have been assigned in a way that makes the corresponding literals false.

In particular, a prefix of the partial assignment may have the same property, that is, there exists an index such that cannot be extended to form a solution with whatever value for .

Once it finds such a snippet, it registers the copyright for that article, obtains a "partial assignment" of copyright from the true rightholder, and then sues the owner of the third-party website.

Especially among smaller districts, it is cost-effective, he said, adding, "If a district needs a partial assignment of a special area teacher like gym or art, it may look to match up with another district in order to share the teacher."

The relator need not have been personally harmed by the defendant's conduct; instead, the relator is recognized as receiving legal standing to sue by way of a "partial assignment" of the injury to the government caused by the alleged fraud.

In Stevens, the Supreme Court also endorsed the "partial assignment" approach to qui tam relator standing to sue, which had previously been articulated by the Ninth Circuit Federal Court of Appeals and is an exception to the general legal rule for standing.

Stevens, 529 U.S. 765 (2000), the United States Supreme Court endorsed the "partial assignment" approach to qui tam relator standing to sue under the False Claims Act - allowing private individuals to sue on behalf of the U.S. government for injuries suffered solely by the government.

In particular, backtracking or some other form of search is run over a number of variables; whenever a consistent partial assignment over these variable is found, inference is run over the remaining variables to check whether this partial assignment can be extended to form a solution.