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More generally, the solution set to an arbitrary collection E of relations (E i) (i varying in some index set I) for a collection of unknowns (), supposed to take values in respective spaces (), is the set S of all solutions to the relations E, where a solution () is a family of values (()) such that substituting () by () in the collection E makes all relations "true".
Software of unknown pedigree (SOUP) is software that was developed with a unknown process or methodology, or which has unknown or no safety-related properties. [1] In the medical device development standard IEC 62304, SOUP expands to software of unknown provenance, and in some contexts uncertain is used instead of unknown, but any combination of unknown/uncertain and provenance/pedigree refer ...
Any problem that can be expressed as a set of well-formed formulas (WFFs) or Horn clauses, and that constitutes a directed graph with one or more sources (that is, hypotheses) and sinks (that is, desired conclusions), can be solved, in principle, by GPS.
The space of all candidate solutions, before any feasible points have been excluded, is called the feasible region, feasible set, search space, or solution space. [2] This is the set of all possible solutions that satisfy the problem's constraints. Constraint satisfaction is the process of finding a point in the feasible set.
Declarative solutions are easier to understand than imperative solutions, [12] and there has been a long-term trend from imperative to declarative methods. [13] [14] Formula calculators are part of this trend. Many software tools for the general user, such as spreadsheets, are declarative. Formula calculators are examples of such tools.
Each free variable gives the solution space one degree of freedom, the number of which is equal to the dimension of the solution set. For example, the solution set for the above equation is a line, since a point in the solution set can be chosen by specifying the value of the parameter z. An infinite solution of higher order may describe a ...
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Conversely, given a solution to the SubsetSumZero instance, it must contain the −T (since all integers in S are positive), so to get a sum of zero, it must also contain a subset of S with a sum of +T, which is a solution of the SubsetSumPositive instance. The input integers are positive, and T = sum(S)/2.