When a Non Jew does something it would work according to Halacha, however when a Jew does the same thing it is useless.
closed as not constructive by Isaac Moses♦ Jun 17 '11 at 21:44
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Negating an avoda zara. If a non-Jew takes an idol and says "I reject this!" and damages it, the idol is no longer prohibited from benefit. A Jew can't do that.
If an animal was mostly slaughtered by a Jew (the majority but not all of the trachea & esophagus were cut) and the animal is not dying, a non-Jew can kill it however he wants and the animal will be kosher. If a Jew shechted the rest of the way, it would be a shihiyah b'miut batra (a pause in the final portion) and the animal is neveila (not kosher). But since the slaughter of a non-Jew is nothing, the majority slaughtered by the Jew is all that counts.
(See Shulchan Aruch YD 23:5)
If a non-Jew does m'lacha for himself on Shabas, a Jew can use the result immediately; not so if a Jew does. (As always, CYLOR.)
A non-jew can taste a mixture of food to tell if the prohibited substance (e.g. milk in meat) inside gave taste.
A non-Jew can run a kosher establishment without the certifiers worrying (as much) about him owning chametz over pesach, toveling all the kelim, etc..