P robabilistically C heckable P roofs Guy Kindler The Hebrew University.

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Presentation transcript:

P robabilistically C heckable P roofs Guy Kindler The Hebrew University

Proofs – why? Proofs problems all around… Math : Homework Identity: passwords suck Credit cards: chip (zero knowledge) Smartness!! Cloud computation Sensitive computation (fission decay) Etc…

What is a proof Euclid: argument based on axioms A committee decides (Fourier 1825) Frege System (1880) Some paradoxes Hilbert’s program (1900) Godel: completeness, incompleteness (1930) Turing: machine verifiable(1936) Machine-generate (1976)

Turing Machine Theoretical computer (1936) Has inputs and outputs TM

Example: Traveling Salesman All cities traversable, length < X US: cities Given proof: easy to verify Finding route: virtually impossible!

Applications Verify mathematics Check homework Check long Proofs (four color theorem) TM

Checking Faster Cook-Levin Theorem (70’s) Each checker reads 3 letters! Problem: reliability TM

Fixing Reliability Problem TM

Fixing Reliability Problem TM

Fixing Reliability Problem TM

Fixing Reliability Problem TM

Fixing Reliability Problem TM PCP Theorem [1992]!

Probabilistic Checking TM Choose few checkers randomly!!

Probabilistic Checking TM Choose few checkers randomly!!

Computation in Cloud 42 Proof

Problems Constructing checkers takes time Proof is long. Many other real-life constraints. But work is still in progress!

Thank You

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