Universal Communication. Brendan Juba (MIT) With: Madhu Sudan (MIT). Setting. 101011110001010. 001100101011101. . . . 1111010110001. WHAT IS BOB GAINING FROM THIS INTERACTION??. TO SEE IF THEY ARE INTELLIGENT ?. TO OBTAIN WISDOM?. WHY WOULD YOU TALK TO AN ALIEN ?.
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Brendan Juba (MIT)
With: Madhu Sudan (MIT)
. . .
WHAT IS BOB GAINING FROM THIS INTERACTION??
WHAT CAN BOB LEARN FROM ALICE?
“Here is a Bob s.t. for every alien languageand every instance x,Bob efficiently learns if xS”
Require Alice be helpful in some language.
Bob is S-Universal if S-helpfulA polynomialp x (of lengthn)whp Bobdecides “xS?” when conversing withA, within p(n)steps in expectation
For any PSPACE-completeS,there is a S-Universalprotocol
If an S-Universalprotocol exists,SPSPACE
(Assuming BPP ≠ PSPACE)For any PSPACE-completeS,if Alice helps a protocol of lengthlthe running time of a S-UniversalBobmust include a constant factorthat isexponential in l
UNIVERSAL COMMUNICATIONis (only) possible for VERIFIABLE GOALS.