Abstract
We observe that a combination of known top-down and bottom-up lower bound techniques of circuit complexity may yield new circuit lower bounds.
An important example is this: Razborov and Wigderson showed that a certain function f in ACC 0 cannot be computed by polynomial size circuits consisting of two layers of MAJORITY gates at the top and a layer of AND gates at the bottom. We observe that a simple combination of their result with the HÃ¥stad switching lemma yields the following seemingly much stronger result: The same function f cannot be computed by polynomial size circuits consisting of two layers of MAJORITY gates at the top and an arbitrary AC 0 circuit feeding the MAJORITY gates.
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Hansen, K.A., Miltersen, P.B. (2004). Some Meet-in-the-Middle Circuit Lower Bounds. In: Fiala, J., Koubek, V., KratochvÃl, J. (eds) Mathematical Foundations of Computer Science 2004. MFCS 2004. Lecture Notes in Computer Science, vol 3153. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-540-28629-5_24
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DOI: https://doi.org/10.1007/978-3-540-28629-5_24
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