Canonical Representations for Direct Generation of Strategies in High-level Petri Games (Full Version)

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.