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 $\ell = q$ the threshold for denoising using gates subject to $q$-ary symmetric noise with error probability $\epsilon$ 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 $\ell < q$, showing that reliable Boolean computation can be performed using $2$-input ternary logic gates subject to symmetric ternary noise of strength $\epsilon < 1/6$ by using the additional alphabet element for error signalling.

翻译：我们给出了关于在物理字母表规模为$q > 2$时使用公式进行可靠计算的两个新正向结果。首先，我们证明当逻辑字母表规模$\ell = q$时，使用受错误概率为$\epsilon$的$q$进制对称噪声影响的逻辑门进行去噪的阈值严格大于布尔计算可能达到的阈值，并且我们展示了一个可在此阈值下可靠计算的$q$进制函数克隆集。其次，我们提供了一个$\ell < q$的示例，表明通过使用额外的字母表元素进行错误信号传递，利用受强度$\epsilon < 1/6$的对称三元噪声影响的二输入三元逻辑门，可以实现可靠的布尔计算。