Another proof that BPP subseteq PH (and more).

We provide another proof of the Sipser--Lautemann Theorem by which BPP ` MA (` PH).The current proof is based on strong results regarding the amplification of BPP , due to Zuckerman.Given these results, the current proof is even simpler than previous ones. Furthermore,extending the proof leads to two results regarding MA: MA ` ZPPNP(which seems to benew), and that two-sided error MA equals MA. Finally, we survey the known facts regardingthe fragment of the polynomial-time hierarchy...