Computational limitations of small-depth circuits
Computational limitations of small-depth circuits
Languages that capture complexity classes
SIAM Journal on Computing
Bounded arithmetic, propositional logic, and complexity theory
Bounded arithmetic, propositional logic, and complexity theory
Logical Foundations of Proof Complexity
Logical Foundations of Proof Complexity
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We show that the bounded arithmetic theory V0does not prove that the polynomial time hierarchy collapses to the linear time hierarchy (without parameters). This result follows from a lower bound for bounded depth circuits computing prefix parity, where the circuits are allowed some auxiliary input.This is a continuation of earlier work by the authors which showed that this collapse is not provable in ${\mbox{\rm{PV}}}$ under a cryptographic assumption.