  Petri games are a multi-player game model for the synthesis problem in
distributed systems, i.e., the automatic generation of local controllers. The
model represents causal memory of the players, which are tokens on a Petri net
and divided into two teams: the controllable system and the uncontrollable
environment. For one environment player and a bounded number of system players,
the problem of solving Petri games can be reduced to that of solving B\"uchi
games.
  High-level Petri games are a concise representation of ordinary Petri games.
Symmetries, derived from a high-level representation, can be exploited to
significantly reduce the state space in the corresponding B\"uchi game. We
present a new construction for solving high-level Petri games. It involves the
definition of a unique, canonical representation of the reduced B\"uchi game.
This allows us to translate a strategy in the B\"uchi game directly into a
strategy in the Petri game. An implementation applied on six structurally
different benchmark families shows in most cases a performance increase for
larger state spaces.
