We prove that polynomial size discrete Hoppeld networks with hidden units compute exactly the class of Boolean functions PSPACE/poly, i.e., the same functions as are computed by polynomial space-bounded nonuniform Turing machines. As a corollary to the construction, we observe also that networks with polynomially bounded interconnection weights compute exactly the class of functions P/poly, i.e...

the excessive biological sludge production is one of the disadvantages of aerobic process such as sbr. so the problem of excess sludge production along with its treatment , and disposal in aerobic processes in municipal and industrial waste water can be seen in many parts of the world even in our country . to solve the problem of excess sludge production , reducing in by oxidizing some of the s...

A long standing open problem in the computational complexity theory is to separate NE from BPP, which is a subclass of NPT(NP) ∩ P/Poly. In this paper, we show that NE 6⊆ NPT(NP ∩ Nonexponentially-Dense-Class), where Nonexponentially-Dense-Class is the class of languages A without exponential density (for each constant c > 0, |A| ≤ 2 c for infinitely many integers n). Our result implies NE 6⊆ N...