Abstract
Arthur-Merlin games were introduced recently by Babai in order to capture the intuitive notion of efficient, probabilistic proof-systems. Considered as complexity classes, they are extensions of NP. It turned out, that one exchange of messages between the two players is sufficient to simulate a constant number of interactions. Thus at most two new complexity classes survive at the constant levels of this new hierarchy: AM and MA, depending on who starts the communication. It is known that \(MA \subseteq AM\). In this paper we answer an open problem of Babai: we construct an oracle C such that \(AM^C - \Sigma _2^{P,C} \ne \emptyset\). Since \(MA^C \subseteq \Sigma _2^{P,C}\), it follows that for some oracle C, MAC≠AMC. Our prooftechnique is a modification of the technique used by Baker and Selman to show that ∑ P2 and ∏ P2 can be separated by some oracle. This result can be interpreted as an evidence that with one exchange of messages, the proof-system is stronger when Arthur starts the communication.
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© 1987 Springer-Verlag Berlin Heidelberg
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Santha, M. (1987). Relativized Arthur-Merlin versus Merlin-Arthur games. In: Nori, K.V. (eds) Foundations of Software Technology and Theoretical Computer Science. FSTTCS 1987. Lecture Notes in Computer Science, vol 287. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-18625-5_66
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DOI: https://doi.org/10.1007/3-540-18625-5_66
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