In mathematics, constraint counting is counting the number of constraints in order to compare it with the number of variables, parameters, etc. that are free to be determined, the idea being that in most cases the number of independent choices that can be made is the excess of the latter over the former.
For example, in linear algebra if the number of constraints (independent equations) in a system of linear equations equals the number of unknowns then precisely one solution exists; if there are fewer independent equations than unknowns, an infinite number of solutions exist; and if the number of independent equations exceeds the number of unknowns, then no solutions exist.
In the context of partial differential equations, constraint counting is a crude but often useful way of counting the number of free functions needed to specify a solution to a partial differential equation.
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In mathematics, constraintcounting is counting the number of constraints in order to compare it with the number of variables, parameters, etc. that are...
unknowns). The terminology can be explained using the concept of constraintcounting. Each unknown can be seen as an available degree of freedom. Each...
Constraint satisfaction problems (CSPs) are mathematical questions defined as a set of objects whose state must satisfy a number of constraints or limitations...
others. The terminology can be described in terms of the concept of constraintcounting. Each unknown can be seen as an available degree of freedom. Each...
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solutions we might optimistically expect, we can appeal to Einstein's constraintcounting method. A typical conclusion from this style of argument is that...
constraint satisfaction problem. In his paper Sudoku as a Constraint Problem, Helmut Simonis describes many reasoning algorithms based on constraints...
counter was initially designed for counting red blood cells, but with later modifications it proved effective for counting white blood cells. Coulter counters...
of constraints. It simply means that it runs shortest path algorithm after pruning those links that violate a given set of constraints. A constraint could...
In theoretical physics, a constraint algebra is a linear space of all constraints and all of their polynomial functions or functionals whose action on...
which generalize countingconstraint satisfaction problems (#CSP). A #CSP instance is a hypergraph G=(V,E) called the constraint graph. Each hyperedge...
minimum, or saddle) throughout the time evolution of the system. This constraint allows the calculation of the equations of motion of the system using...
generalizations of the mutual information. It is also known as the multivariate constraint (Garner 1962) or multiinformation (Studený & Vejnarová 1999). It quantifies...
common. The back-vowel constraint is also triggered by labial clicks, though not by labial stops. Clicks subject to this constraint involve a sharp retraction...
a set of non-divisible projects or tasks under a fixed budget or time constraint, respectively. The knapsack problem has been studied for more than a century...
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