The phrase "a constraint exists" is correct and usable in written English.
You can use it when discussing limitations or restrictions in a particular context, such as project management, research, or problem-solving.
Example: "In our analysis, we found that a constraint exists that limits our ability to expand the project scope."
Alternatives: "a limitation is present" or "a restriction is in place."
The result of applying this method is the complete set of non-empty C-induced subtraces of sequences sorting π into π T. Generally, we have no guarantee that a sorting sequence that respects all constraints exists, thus this approach can lead to an empty result.
On the other hand, soft constraints may allow for unnecessary violations of the original constraints, i.e., the constraints may be violated even if a valid solution that does not violate any constraints exists.
In order to show a contradiction, we assume that no such local constraint exists.
However, no such constraint exists when ribulose-5-phosphate ribulose-5-phosphate ribulose-5-phosphates vis the rearrangement reactions oformednon-oxidative pentose-phosphate pathway.
The constraint-based algorithm forces this requirement to be obeyed whenever a sufficient number of constraints exists.
In Additional file 5, Figure S8 for simplicity we consider the reduction of a single-clause satisfaction problem to finding if a minimal hyperpath satisfying the constraints exists.
The boolean assignments σ i = v i * are a solution of the 3-SAT problem and, inversely if a solution of the 3-SAT problem exists then a minimal pathway satisfying the constraints exists and is the one obtained using only one of the hyperarcs for each X j among the ones whose head only contains ν j and vertices v i *.
In fact, if the output of Minimize is an empty set then there are no minimal hyperpaths satisfying the constraints; however if the output is a minimal hyperpath then obviously a minimal constrained hyperpath exists; and finally, if the output is a non-minimal hyperpath then we do not know if a minimal hyperpath satisfying the constraints exists or not.
