I would like to translate some simple programming operation in mathematical equation.
I am very new to formalisation.
I would like to describe these 2 sequences formally. I am not really sure how to start. This is what I came up with :
Let $\varpi$ be a dummy vector such as
$\varpi_{t}= \begin{cases} 1 & \quad \text{if Done} \\ 0 & \quad \text{if Not Done} \\ \end{cases}$
Let $A$ and $B$ represent two sequences of $\varpi$ both belonging to a related unit $c$. Time (or the position along the sequence) is represented by $t$ with $t = (1, 2, t,\dots, t_{-1}, T = 10)$, where $T$ is the sequence length or the last position of the sequence.
$\xi_{c}$ represents the matched $\varpi_{t}$ for both sequences.
$\xi_{c} = \begin{cases} 1 & \quad \text{if } A\varpi_{t} = B\varpi_{t} \\ 0 & \quad \text{if } A\varpi_{t} \neq B\varpi_{t}\\ \end{cases}$
$\vartheta_{c}$ represents the combined length of $\varpi_{t}$ sequences.
$\vartheta_{c} = \begin{cases} 1 & \quad \text{if } A\varpi_{t} | B\varpi_{t} \\ 0 & \quad \text{Other}\\ \end{cases}$
Finally, $o_{c}$ is the inverse of $\xi_{c}$. (How can I write this simply?)
I wonder how to correctly write operation such as OR | and also AND &.
Is it good practice to do that or not ?
$ \xi_{c} = \begin{cases} 1 & \quad \text{if } A\varpi_{t} = B\varpi_{t} \\ 0 & \quad \text{if } A\varpi_{t} \neq B\varpi_{t}\\ \end{cases} $
Any correction or suggestion ?