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If it turns out that a problem is equivalent to a known open problem, then the open-problem tag is added. After that, the question essentially becomes, "What is known about this problem? What are some possible ways to approach this problem? What are some ways that people have tried to attack it before, and with what results?"
3
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Conjecture of a subset of Wang tile which might be decidable
If you're interested in restriction of the domino problem to tile sets with some determinism properties, you might also be interested in this result about 4-way deterministic tile sets.