A characterization of the (natural) graph properties testable with one-sided error

@article{Alon2005ACO,
  title={A characterization of the (natural) graph properties testable with one-sided error},
  author={Noga Alon and Asaf Shapira},
  journal={46th Annual IEEE Symposium on Foundations of Computer Science (FOCS'05)},
  year={2005},
  pages={429-438}
}
The problem of characterizing all the testable graph properties is considered by many to be the most important open problem in the area of property-testing. Our main result in this paper is a solution of an important special case of this general problem; Call a property tester oblivious if its decisions are independent of the size of the input graph. We show that a graph property P has an oblivious one-sided error tester, if and only if P is (semi) hereditary. We stress that any "natural… CONTINUE READING
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