Abstract
We show that the following relationships hold:
where the inclusions are strict.
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References
M. Ajtai, ∑ 21 -formulae on finite structures, Ann. Pure Appl. Logic 24 (1983) 1–48.
S.R. Buss,Bounded Arithmetic (Bibliopolis, 1986). Revision of Ph.D. dissertation, Princeton University (1985).
M. Furst, J.B. Saxe and M. Sipser, Parity, circuits, and the polynomial-time hierarchy, Math. Sys. Theory 17 (1984) 13–27.
J. Håstad, Computational limitations for small depth circuits, PhD thesis, MIT (1986).
N. Immerman, Expressibility and parallel complexity (1987; revised August 1988).
I. Wegener,The Complexity of Boolean Functions (Wiley-Teubner series in Computer Science, Stuttgart, 1987).
A.C. Yao, Separating the polynomial time hierarchy by oracles: Part I,Proc. 26th Annual IEEE Symp. on Foundation of Computer Science (1985) pp. 1–10.
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Mantzivis, SG. Circuits in bounded arithmetic part I. Ann Math Artif Intell 6, 127–156 (1992). https://doi.org/10.1007/BF01531025
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DOI: https://doi.org/10.1007/BF01531025