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CS 5800

Explore the concept of viewing constructive proofs as algorithms and understand the strategies behind winning semantic games. Discover interesting recurrences and asymptotic bounds for solving HSRnk with constant k.

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CS 5800

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  1. CS 5800 Karl Lieberherr

  2. Proofs as Algorithms • It is beneficial to view the constructive proofs we do in this course as algorithms. Why is a proof an algorithm? A proof is a defense strategy to systematically win in a semantic game. The defense strategy = algorithm tells you: • which values to choose, based on values chosen earlier. • which side of a Boolean connective to choose.

  3. Negation • Note that if the claim contains a negation, you need to play both verifier and falsifier roles.

  4. k=1: T(q) = T(q-1)+1 ,T(1)=2, T(q)=q+1 • Muster Theorem: a=1, b=1, d=0 • O(q) (middle case) • Guess: T(q) <=c*q • T(q)<=c(q-1)+1 <= c*q if c>=1

  5. k=2: U(q)=U(q-1)+q, U(1)=2 • Muster Theorem: a=1,b=1,d=1 • O(q2) (middle case)

  6. HSR((2^q)-1,q-1)=qHSR(2^q,q)=q • What are the interesting recurrences behind HSR? • What are interesting asymptotic bounds for HSR? • constant k: how fast is the number of questions for solving HSRnk growing as a function of n?

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