Hamming similarity for sequences

Definition
Given two squences (or strings) of symbols in an alphabet $$\mathcal{L}$$, the Hamming similarity is a function $$HammingSim:\mathcal{L}^*\times\mathcal{L}^*\longrightarrow [0,1]$$ that measures the number of positions for which the corresponding symbols are equals, divided by the length of the bigest sequence:



HammingSim(s,t)=\frac{\sum_{i=1}^{\min\{|s|,|t|\}}IdSim(s[i],t[i])}{\max\{|s|,|t|\}}, $$

where $$IdSim$$ is the Identity similarity.

Examples

 * HammingSim('house','horse') = 4/5 = 0.8.
 * HammingSim('abcd',' ') = 0/4 = 0.
 * HammingSim('abcd','a') = 1/4 = 0.25.
 * HammingSim('abcd','b') = 0/4 = 0.
 * HammingSim('id0345','id1352') = 3/6 = 0.5.

Normalization
It is normalized.

Applications

 * Comparing codes.