Super-polynomial versus half-exponential circuit size in the exponential hierarchy

Authors:
Peter Bro Miltersen;N. V. Vinodchandran;Osamu Watanabe
Affiliations:
BRICS, Department of Computer Science, University of Aarhus;BRICS, Department of Computer Science, University of Aarhus;Department of Mathematical and Computing Sciences, Tokyo Institute of Technology, Ookayama, Tokyo
Venue:
COCOON'99 Proceedings of the 5th annual international conference on Computing and combinatorics
Year:
1999

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Abstract

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.