universal communication l.
Download
Skip this Video
Loading SlideShow in 5 Seconds..
Universal Communication PowerPoint Presentation
Download Presentation
Universal Communication

Loading in 2 Seconds...

play fullscreen
1 / 31

Universal Communication - PowerPoint PPT Presentation


  • 192 Views
  • Uploaded on

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 ?.

loader
I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
capcha
Download Presentation

PowerPoint Slideshow about 'Universal Communication' - Faraday


Download Now An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.


- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript
universal communication

Universal Communication

Brendan Juba (MIT)

With: Madhu Sudan (MIT)

setting
Setting

101011110001010

001100101011101

. . .

1111010110001

WHAT IS BOB GAINING FROM THIS INTERACTION??

why would you talk to an alien

TO SEE IF THEYARE INTELLIGENT?

TO OBTAINWISDOM?

WHY WOULD YOU TALKTO AN ALIEN?

TO ASK THEM TO STOP BOMBARDINGUS WITH DANGEROUS RADIATION??

motivation
Motivation

WHAT CAN BOB LEARN FROM ALICE?

setting6
Setting
  • Fix a setS and a stringx
  • Bob wishes to learn “xS?”
  • WANT: protocol that terminates with a verdict that is CORRECT (whp)
  • Also: efficient in length of x
outline
Outline
  • Definition: Universal protocol
  • Analysis of communicating wisdom
  • Generalizing goals
we want a theorem of the form

We want a theorem of the form

???

“Here is a Bob s.t. for every alien languageand every instance x,Bob efficiently learns if xS”

language
Language???

X

  • Grammar?
  • Terms?
  • Strings with interpretations

STRONG ASSUMPTIONS!

observation

I COULD HELP,IF I WANTED.

Observation

Some Alices are unhelpful.

x∈S?

y∈S?

z∈S?

solution
Solution

Require Alice be helpful in some language.

xS?

xS

observation12

WHAT’S THE PASSWORD?

Observation

Some Alices are stillunhelpful.

HELLO??

@&^#*&^%$; x?

xS

I’M NOT TALKINGTO YOU ANYMORE.

revision
Revision
  • Require that some B’ can efficientlydecide “xS?” with Alice’s assistance,independent of prior message history
  • Henceforth, such Alices will be called S-helpful
definition s universal
Definition: S-Universal

Bob is S-Universal if S-helpfulA polynomialp x (of lengthn)whp Bobdecides “xS?” when conversing withA, within p(n)steps in expectation

outline15
Outline
  • Definition: Universal protocol
  • Analysis of communicating wisdom
  • Generalizing goals
main idea 1
MAIN IDEA #1
  • We can efficientlyenumerate and runallefficient protocols
  • If A is S-Helpful, she helps an efficient protocolB’ that appears in the enumeration
main idea 2
MAIN IDEA #2
  • If we can get a proof of either xS or xS, we can guarantee correctness
  • If SIP, such proofsexist
  • If S is PSPACE-complete, we can reduce proving (non)membershipto other instances of S
theorem
Theorem

For any PSPACE-completeS,there is a S-Universalprotocol

limitation 1 main observation
Limitation 1: main observation
  • Suppose that for somex,some malicious alien Alicecan misleadBob (whp)
  • We can convert Alice into a “helpful” A’who stillmisleadsBob: pad the useful queries
  • Recall: a S-UniversalBobshould not be misled by a S-HelpfulAlice!
limitation 1 finishing up
Limitation 1: finishing up
  • Thus: a S-UniversalBob 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 decideS
first limitation
First limitation

If an S-Universalprotocol exists,SPSPACE

second limitation
Second limitation

(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

outline24
Outline
  • Definition: Universal protocol
  • Analysis of communicating wisdom
  • Generalizing goals
what about efficiency
What about efficiency?
  • Our construction obtained wisdom from an Alice who could decide PSPACE
  • We obtain analogous results with efficientAlices: 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
General setting
  • SOME interactions are successful, others are NOT.
  • We seek a protocol that tells us how to engage in successfulinteractions (whp)
define goal
Define: “goal”
  • Efficiently verifiablesufficientconditions 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
(technical) CONCLUSION

UNIVERSAL COMMUNICATIONis (only) possible for VERIFIABLE GOALS.

practical motivation
Practical motivation
  • Designing protocols for individual devices. (cf. sets, pairs, etc.)
  • Simpler, more robust networks
practical technical challenges
Practical technical challenges
  • Design suitable “goals” (think: “program checking”)
  • Find a restricted class of protocols that permits “length-efficient” setup
thank you

Thank you!

Questions?