algorithm for checking satisfiability
Here is how I would do it: 
Algo: Verifier for DNF-SAT problem given as array of closures and a possible mapping of literals to booleans
Input:
Array of closures: [$C_1$,$C_2$,...,$C_m$] 
where $C_j \subseteq \{x_1,...,x_n,\neg x_1, ... \neg x_n\}$
(Certificate) Array $M$ where $M_i$ is the boolean value of literal $x_i$ 
Output: true or false
for $i = 1$ to $m$:
  value = true
  for literal in $C_i$:
    if literal == $x_i$:
      value = value or $M[i]$:
    else if literal == $\neg x_i$:
      value = value or (not $M[i]$)
  if not value:
    return false
return true 

Note: the math notation is indented and commonly used in pseudocode sadly cs stackexchange doesn't support it