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Tragedy of Theorem Proving

This paper explores the challenges in theorem proving through linear implementation and a hairpin example. It discusses strategies for amplifying non-empty clauses and tackling the issue of using goal literals multiple times. Examples are provided to illustrate the concepts. The text also suggests possible solutions such as removing partial double strands and using beads for each literal, with specific bead separation recommendations based on the number of variables. The question of whether a protein that binds to only a single strand exists is considered.

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Tragedy of Theorem Proving

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  1. Tragedy of Theorem Proving 2002. 07. 12

  2. In Linear Implementation • Non-empty clause can be amplified!

  3. GACT TGCA ACGT GAGT CAAT CTGA ¬Q ¬P R ¬S ¬T Q ACGT TGAC P ¬R GACT TGCA ACGT ¬P R GAGT CAAT CTGA ¬S ¬T Q ACGT TGAC P ¬R GACT TGCA ACGT GAGT CAAT CTGA ACGT TGAC ¬S ¬T Q P ¬R Example Can be amplified with primer S and R

  4. In Hairpin Implementation • If goal literal is used more than once

  5. Example ¬Q Q ¬P ¬S S R ¬R R R R ¬R ¬P Q S ¬S ¬P ¬Q ¬S S ¬R ¬R R R

  6. Possible Solution • Both implementation have the same problem • Remove partial double strands • Use beads for each literal…(-_-) • 2v bead separations (v: number of variables) • 수율 문제 • Protein that binds to only single strand • Exists?

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