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Consistency of circuit lower bounds with bounded theories

2019
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Logical Methods in Computer Science
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Proving that there are problems in $\mathsf{P}^\mathsf{NP}$ that require boolean circuits of super-linear size is a major frontier in complexity theory. While such lower bounds are known for larger complexity classes, existing results only show that the corresponding problems are hard on infinitely many input lengths. For instance, proving almost-everywhere circuit lower bounds is open even for problems in $\mathsf{MAEXP}$. Giving the notorious difficulty of proving lower bounds that hold for

doi:10.23638/lmcs-16(2:12)2020
fatcat:lxc3twx6pjhadaymq4fflw4mvu