Super-Polynomial Versus Half-Exponential Circuit Size in the Exponential Hierarchy

Lower bounds on circuit size were previously established for functions in Σ2p, ZPPNP, Σ2exp, ZPEXPNP and MAexp. We investigate the general question: Given a time bound f(n). What is the best circuit size lower bound that can be shown for the classes MA-TIME[f], ZP-TIMENP[f], ... using the techniques currently known? For the classes MAexp, ZPEXPNP and Σ2exp, the answer we get is "half-exponential". Informally, a function f is said to be half-exponential if f composed with itself is exponential.

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