We present two new positive results for reliable computation using formulas
over physical alphabets of size q>2. First, we show that for logical
alphabets of size â„“=q the threshold for denoising using gates subject to
q-ary symmetric noise with error probability ϵ is strictly larger
that possible for Boolean computation and we demonstrate a clone of q-ary
functions that can be reliably computed up to this threshold. Secondly, we
provide an example where â„“<q, showing that reliable Boolean computation
can be performed using 2-input ternary logic gates subject to symmetric
ternary noise of strength ϵ<1/6 by using the additional alphabet
element for error signalling.Comment: 14 pages, 2 figure