<p>In a safety game, the existence of a maximally permissive strategy is easy to show: you always allow all moves that stay in the winning region.
This works because safety games are precisely the games where a play staying in the winning region is guaranteed to be winning itself. Moreover such a strategy is clearly maximally permissive, by definition of the winning region.</p>

CC BY-SA 4.0
2021-10-08T23:53:10.310Z
2021-10-08T23:53:10.310Z
Denis
<p>Different definitions of maximally permissive strategies exist. For instance, in <a href="https://www.labri.fr/perso/igw/Papers/igw-perm.ps" rel="nofollow noreferrer">(Bernet, Janin, and Walukiewicz 2002)</a>, strategies are compared by looking at inclusion of the behaviors/outcomes they allow. In particular, a maximally permissive strategy N is a non-deterministic strategy such that there is no other non-deterministic strategy N_1 that allows more behaviors/outcomes than N.</p>
<p>Moreover, it is known that in a safety game Player 0 (let's call it the protagonist) has a maximally permissive strategy. It is also known that if a game G has a maximal permissive strategy then G can be reduced to a safety game.</p>
<p>My question is: there should be a theorem claiming the existence of maximally permissive strategies for safety properties, is it proved in some paper?</p>

<linear-temporal-logic><omega-language>
Maximally Permissive Strategies for Safety Properties
kafka
# Maximally Permissive Strategies for Safety Properties

(Asked by: username_0 on 2021-09-28)

Different definitions of maximally permissive strategies exist. For instance, in [(Bernet, Janin, and Walukiewicz 2002)](https://www.labri.fr/perso/igw/Papers/igw-perm.ps), strategies are compared by looking at inclusion of the behaviors/outcomes they allow. In particular, a maximally permissive strategy N is a non-deterministic strategy such that there is no other non-deterministic strategy N\_1 that allows more behaviors/outcomes than N.

Moreover, it is known that in a safety game Player 0 (let's call it the protagonist) has a maximally permissive strategy. It is also known that if a game G has a maximal permissive strategy then G can be reduced to a safety game.

My question is: there should be a theorem claiming the existence of maximally permissive strategies for safety properties, is it proved in some paper?

**Tags:** linear-temporal-logic, omega-language

---

## 1 answers

### Answer by username_1 on 2021-10-08. Score: 1

In a safety game, the existence of a maximally permissive strategy is easy to show: you always allow all moves that stay in the winning region.
This works because safety games are precisely the games where a play staying in the winning region is guaranteed to be winning itself. Moreover such a strategy is clearly maximally permissive, by definition of the winning region.


---

