# Compute deadends and reachable states symbolically

Hi,

I saw couple of questions from previous year questions papers and final exercise sheet, where it is asked to compute reachable states/dead ends symbolically. However, when I went through exercise sheet and slides, I could find the ways to find predecessor/successors only through symbolically not the deadends/reachable states. I am not sure if I have missed them somehow. Could you please let me know the steps to obtain the same?

The formula []false holds exactly on those states that do not have outgoing transitions. Hence, you can compute these states of a structure by computing the universal predecessors of false.

The reachable states are those that are (1) initial states or (2) reachable from a reachable state. That gives rise to the definition in ยต-calculus mu y. (Init | <:>y) which means that you can compute the reachable states by a fix point iteration as given by the above formula, i.e., start with the initial states, then always add existential successor states of the states that you already have.
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Thanks Professor for the quick reply. It is clear now (y)