# Single verb for make something equivalent

Is there a single verb meaning to make something equivalent to something? I want to use this possibly existent word to express the following:

"We transformed Problem A into the following problem B, which is proved equivalent to Problem A."

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How would you use the word you're asking for? Could you provide a sample sentence with a blank in it? – Andrew Leach Jul 12 '14 at 18:23
I'm more familiar with 'Problem A and Problem B were known to exist; solving problem B was proved to be equivalent to solving problem A'. (Doesn't this arise with Fermat's Last?) – Edwin Ashworth Jul 12 '14 at 20:08
Just say "We proved problem A and problem B were equivalent." Do you need to use a word like "equivalentized"? – Peter Shor Aug 27 '15 at 11:56

Per the Cambridge Dictionary, to equate means:

to consider one thing to be the same as or equal to another thing.

while to equalize (UK: equalise):

to make things or people equal.

To correspond:

to be similar or the same in some way:

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Depending on context, normalize may also be used. – Wayfaring Stranger Jul 12 '14 at 22:33

To equalize:

• To make uniform.
• make equal, uniform, corresponding, or matching: let's equalize the duties among all employees in our office.
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Mathematicians use rearrange as a verb when they transform one equation into an equivalent equation.

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Thanks it is mathematics! However, a conjecture is it, rather than an equation. – kwgl Jul 12 '14 at 19:51
@kwgl In that case, reformulate might work (e.g. from Stack Exchange Mathematics: Reformulating the Goldbach conjecture in a quasi-Pythagorean form). – D Krueger Jul 13 '14 at 0:37

In topics such as NP-completeness, the word reduce is used in the following sense:

Reduce transitive verb 9b : to transpose from one form into another : convert - M-W

Interestingly, NP-complete problems are said to reduce to one another. More generally:

In computability theory and computational complexity theory, a many-one reduction is a reduction which converts instances of one decision problem into instances of a second decision problem. - Wikipedia

To say that Problem B reduces to Problem A carries the idea that Problem B can be proved to be equivalent to A.

Note that the negation of the reduce doesn't quite correspond to the negation of the idea. "Problem C does not reduce to Problem D" carries the idea that Problem C can be proved to be different from Problem D. If the equivalence is unknown (i.e. not provably equivalent and not provably different), one can say that Problem E has not been shown to reduce to Problem F.

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Equivalent and equal are not the same in mathematics. So "equalize" is not acceptable. Is there such a thing as "equivalize" ?

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