Abstract:We consolidate two widely believed conjectures about tautologiesno optimal proof system exists, and most require superpolynomial size proofs in any system-into a p-isomorphism-invariant condition satisfied by all paddable coNP-complete languages or none. The condition is: for any Turing machine (TM) M accepting the language, P-uniform input families requiring superpolynomial time by M exist (equivalent to the first conjecture) and appear with positive upper density in an enumeration of input families (implies … Show more
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