Arthur - Merlin Games and the Polynomial Time Hierarchy
نویسندگان
چکیده
In this lecture we first discuss bounded-round interactive proof systems and its relationship with other complexity classes. Along the way we prove an interesting result that coNP is not in AM unless the polynomial time hierarchy collapses to its second level. Given GNI has an AM protocol, this gives strong evidence that GI is not NP-complete. As it is unlikely that coNP has bounded round interactive proof, it was open for quite a while whether coNP has IPS at all. Actually complexity theorists come up with a relativized world in which coNP indeed does not have IPS. However, as it turns out and somewhat surprisingly, not only coNP has IPS but also every language in PSPACE does. Given the other direction that IP ⊆ PSPACE, we now know that the power of IP equals the power of PSPACE. We prove both of these results in the final part of this lecture.
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