MAIN IDEA #1 We can efficiently enumerate and run all efficient protocols If A is S-Helpful, she helps an efficient protocol B’ that appears in the enumeration
MAIN IDEA #2 If we can get a proof of either x S or x S, we can guarantee correctness If S IP, such proofs exist If S is PSPACE-complete, we can reduce proving (non)membership to other instances of S
Theorem For any PSPACE-complete S, there is a S-Universal protocol
For how large a class of sets can we exhibit a universal protocol?
Limitation 1: main observation Suppose that for some x, some malicious alien Alice can mislead Bob (whp) We can convert Alice into a “helpful” A’ who still misleads Bob: pad the useful queries Recall: a S-Universal Bob should not be misled by a S-Helpful Alice!
Limitation 1: finishing up Thus: a S-Universal Bob satisfies a strong soundness condition In PSPACE we can find the messages that maximize the probability that Bob halts quickly Since Bob is sound, his verdict on these messages decide S
First limitation If an S-Universal protocol exists, S PSPACE
Second limitation (Assuming BPP ≠ PSPACE) For any PSPACE-complete S, if Alice helps a protocol of length l the running time of a S-Universal Bob must include a constant factor that is exponential in l
What about efficiency? Our construction obtained wisdom from an Alice who could decide PSPACE We obtain analogous results with efficient Alices: limit resources used by our interpreter Depending on resources used to verify, may only be meaningful in an online sense: “Bob converges to a non-trivial interpreter”
General setting 1.SOME interactions are successful, others are NOT. 2.We seek a protocol that tells us how to engage in successful interactions (whp)
Define: “goal” Efficiently verifiable sufficient conditions on Bob’s view of interaction E.g., effective, efficient protocols! Easy generalization of our definitions and universal protocol for the computational goal to any such goal
(technical) CONCLUSION UNIVERSAL COMMUNICATION is (only) possible for VERIFIABLE GOALS.
Practical motivation Designing protocols for individual devices. (cf. sets, pairs, etc.) Simpler, more robust networks
Practical technical challenges 1.Design suitable “goals” (think: “program checking”) 2.Find a restricted class of protocols that permits “length-efficient” setup