An algorithm to compute a set of states that satisfy a specific CTL formula Working through a past exam question and I'm unsure where to start or what form they want the answer in: 

Define an algorithm that receives as input a finite transition
system TS defined over the set of actions {a, b, c} and computes 
the set of states of TS that satisfy the CTL formula ∃a U b.

Would anybody be able to give me a kick-start or a walk-through on how to answer this? Really appreciate any help. 

edit: My attempt based on Klaus' answer

for all executions in TS
 for all states
  if **b** holds 
   add current state to the stack, EXISTS = TRUE
  else if **a** holds
   if current state == next state in execution 
    do nothing
   else if next state contains **a** or **b** 
    add current state to the stack, EXISTS = TRUE
   else 
    do nothing
The set of states satisfying $\exists a U b$ is the smallest set $S$ such that


$S$ contains all states satisfying $b$, and
$S$ contains all states satisfying $a$ which have a successor in $S$


Note that we specify the "smallest" such set because otherwise you could  pick the set of all states, or include arbitrary cycles of $a$-states, etc. Do you see how to get an algorithm from this?