Abstract
A very recent paper by Caussinus, McKenzie, Thérien, and Vollmer [CMTV95] shows that ACC0 is properly contained in ModPH, and TC0 is properly contained in the counting hierarchy. Thus, [CMTV95] shows that there are problems in ModPH that require superpolynomialsize uniform ACC0 circuits, and problems in the counting hierarchy that require superpolynomial-size uniform TC0 circuits. The proof in [CMTV95] uses “leaf languages” as a tool in obtaining their separations, and their proof does not immediately yield larger lower bounds for the complexity of these problems. In this paper, we give a simple direct proof of these same separations, and use it to provide “sub-subexponential” size lower bounds on the size of uniform circuits for these problems.
Supported in part by NSF grant CCR-9509603.
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© 1996 Springer-Verlag Berlin Heidelberg
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Allender, E. (1996). A note on uniform circuit lower bounds for the counting hierarchy (extended abstract). In: Cai, JY., Wong, C.K. (eds) Computing and Combinatorics. COCOON 1996. Lecture Notes in Computer Science, vol 1090. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-61332-3_145
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DOI: https://doi.org/10.1007/3-540-61332-3_145
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