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Arithmetization II

“We Need To Go Deeper”

Photo by Iswanto Arif on Unsplash

Recap

Queries and Error Correction Codes

Toy Example: Boolean Execution Trace

  1. The execution trace has 512 rows, each row containing a single cell with either zero or one in it.
  2. The polynomial constraint we use here is simply AᵢAᵢ-Aᵢ=0, where Aᵢ denotes the i-th cell in this single-column execution trace (a number is equal to its square if and only if it is either 0 or 1).

Roots of Polynomials

Putting It Together

Fibonacci

Translate to Polynomials

Succinctness

More Constraints, More Columns!

Wrapping Up

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