Abstract

ounting arguments that establish upper and lower bounds on the maximum circuit complexity of any n- argument Boolean function over the full basis of 2-input gates. These and closely related results appear in [4, 12, 23, 25]. The particularly slick proof of Theorem 1.1 is due to Schnorr [20]. ffl Section 2 uses Turing time complexity T (n) to bound circuit complexity for families of Boolean functions. Savage [18] showed that the circuit complexity is at most O(T (n) 2 ). Here I present a result with Pippenger that reduces this bound to O(T (n)) for oblivious Turing machines and to O(T (n) log T (n)) for unrestricted Turing This research was supported in part by the National Science Foundation under research grant GJ-43634x

Citations