# A word for the meaning of “over-constrained”

I want to express that I constrained something too much such that it is contradictory now. At first sight, over-constrained seems to fit, but I am not sure whether it is fine to use in a scientific publication. Can you help me?

• It's fine to use in a scientific publication, though if you're using it with respect to something mathematical (like a system of differential equations), be sure to use it correctly. Mathematics tends to have definitions. – Cascabel Nov 10 '10 at 3:00

I've seen over-constrained used several times in scientific publications, referring to a system constrained to such a point that a solution does not exist. So I think you're fine.

(As an example, there's a paper entitled "A brief overview of over-constrained systems" by Michael Jampel published in Springer's Lecture Notes in Computer Science. See it here)

I have never used this word, but I think that “overconstrained” (for a system of equations) is used in two slightly different meanings:

1. There are more constraints than the degree of freedom.
2. There are more constraints than the degree of freedom and there are no solutions because of that.

For example, we can call a system of linear equations with 10 variables and 11 equations “overconstrained” in the sense 1, but it may have a solution if some of the equations are redundant. If you need a precise meaning, I think that you should define the meaning which you intend.

• This is an interesting fact I haven't thought about yet. Thanks! – Rupert Jones Nov 9 '10 at 16:44

I quite like 'shackled' in this context. The implication is that the constraints are like chains/handcuffs.

Tsuyoshi Ito is correct, there are two implications of overconstrained.

In engineering, a bridge design would be overconstrained, for example, if it were rigidly attached at each end of the span. In this case, the force on the connections would be indeterminate and is a bad thing (which is why one side is usually pinned and the other on a roller - to ease a constraint). This usage is the kind meaning there is no result.

Also in engineering and mathematics, overconstrained is used when there are too many simultaneous equations to result in an exact solution. For example, fitting a line to many points is overconstrained because technically a line cannot be drawn simultaneously through all of the points. This, however is a good thing and the solution to this overconstrained system is called a "least-squares" solution, meaning the line is found that has the minimum error from the points (with minimum defined a certain way). This is called the best-fit line and, like I said, this is actually a good thing and the solution is a good solution, especially when the data are noisy.

• Use citations in answers, if you please. – lbf Mar 28 '18 at 3:25