CNS/CS/EE 188a Computation Theory and Neural Systems (Winter 2001)

Homeworks

• LT Calculator. Our solution.

Open problems

• TH² = LT₂ ^ SYM? We know that TH¹ = LT₁ ^ SYM and TH2 < LT2 ^ SYM. Here TH² means symmetric functions with no more than 2 transitions (T(f) <= 2).
• Find AON circuit with less than 18 gates for XOR with 8 variables. No depth restriction. (Theoritical lower bound is 16, and we now can do it by 18. Matt Cook proved that 8 instead of 7 is the minimum number of gates for 4 variables.)
• Given T(f) (or something similar), find a lower bound for arbitrary layered LT circuits. For layered LT circuit with TH gates in the first layer, the lower bound is T(f)+1.