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Certify initial formula

uh yeah proving that random cnf is unsatisfiable okay great um yeah so just interrupt me whenever you have questions i made slides because i'm going to give a more general talk about this simon's in a couple weeks so yeah especially if you have any comments let me know either during or after yes i want to talk about a random random instances of unsat formulas and uh how hard or why is it hard to prove them even though they're in abundance okay so first of just some basic background uh so unset just define that to be the set of all unsatisfiable cnf formulas and we're going to define a proof system propositional proof system for onset as it was defined by cook and wreck house so that it basically is general enough to include any np algorithm so the way they defined it is a basically checks to see if something is a proof so it's a it's a polytime algorithm p that takes strings to unset formulas and you should think of p as taking an encoding of a proof in some standard proof system and then returning whatever it is that it's proving and i'm going to in general use proof and like refutation and proof in the same way so if i'm talking about an onset formula when i say proof or refutation i mean refuting the onset formula or proving its onset and if it's a tautology then when i say proof i mean proving it's a tautology so anyways a proof system you can just view it as a polynomial time procedure that takes as input a string and the range of p is a set of all unsat formulas that's completeness uh well actually soundness and completeness so we want the case that if f is in onset so the the fact that it's uh onto is completeness so if for any f that's unset there has to be a string y or a proof such that p on y outputs f and since the range is just the unsight formulas that's why it's sound so you don't want to have proofs of things that aren't on set does that make sense so again you can think of p as just a non-deterministic procedure that guesses the string y and then verifies that it's whether or not it's a legal proof of so given an unstep formula f p a non-deterministic procedure could guess the string y and then check to see if it's a proof okay and p is polynomially bounded if every onset formula has a string y or has a proof of length polynomial in the length of f okay is that good so far i'll keep going if nobody says anything okay so that's sort of a general definition of what a proof system is and it incorporates pretty much every proof system that we almost every proof system that we know of all the standard...