Lecture monday week 7

<h1>Lecture monday week 7</h1>

Don't do the MDP part yet of the tutorial. Wednesday **presenting project results**. If $P$ is a probability matrix. The matrix $P^n$ tells you what the probabilities are after $n$ steps. If $u$ is the current probability vector of where your are

$$u'^T= u^T \cdot P$$ 

If $v$ is where you want to be $P\cdot v$ gives you the chance that if you start at position $i$ you end up in something inv $v$

**Reminder:** a U b has the condition that condition b has to be reached whilest a W b has not 

$$P_{\geq 1}[\neg a \cup b] \neq A[\neg a \cup b]$$

this is because a certain path could have a probability of zero.


**Bounded until:**

$$(\phi_1 U^{\leq k} \phi_2)$$ 

$\phi_2$ should have been true after $k$ steps.