In the synthesis of distributed systems, we automate the development of distributed programs and hardware by automatically deriving correct implementations from formal specifications. For synchronous distributed systems, the synthesis problem is well known to be undecidable. For asynchronous systems, the boundary between decidable and undecidable synthesis problems is a long-standing open question. We study the problem in the setting of Petri games, a framework for distributed systems where asynchronous processes are equipped with causal memory. Petri games extend Petri nets with a distinction between system places and environment places. The components of a distributed system are the players of the game, represented as tokens that exchange information during each synchronization. Previous decidability results for this model are limited to local winning conditions, i.e., conditions that only refer to individual components. In this paper, we consider global winning conditions such as mutual exclusion, i.e., conditions that refer to the state of all components. We provide decidability and undecidability results for global winning conditions. First, we prove for winning conditions given as bad markings that it is decidable whether a winning strategy for the system players exists in Petri games with a bounded number of system players and one environment player. Second, we prove for winning conditions that refer to both good and bad markings that it is undecidable whether a winning strategy for the system players exists in Petri games with at least two system players and one environment player. Our results thus show that, on the one hand, it is indeed possible to use global safety specifications like mutual exclusion in the synthesis of distributed systems. However, on the other hand, adding global liveness specifications results in an undecidable synthesis problem for almost all Petri games.

Abstract Developing algorithms for distributed systems is an error-prone task. Formal models like Petri nets with transits and Petri games can prevent errors when developing such algorithms. Petri nets with transits allow us to follow the data flow between components in a distributed system. They can be model checked against specifications in LTL on both the local data flow and the global behavior. Petri games allow the synthesis of local controllers for distributed systems from safety specifications. Modeling problems in these formalisms requires defining extended Petri nets which can be cumbersome when performed textually. In this paper, we present a web interface (The web interface is deployed at http://adam.informatik.uni-oldenburg.de .) that allows an intuitive, visual definition of Petri nets with transits and Petri games. The corresponding model checking and synthesis problems are solved directly on a server. In the interface, implementations, counterexamples, and all intermediate steps can be analyzed and simulated. Stepwise simulations and interactive state space generation support the user in detecting modeling errors.

The correctness of networks is often described in terms of the individual data flow of components instead of their global behavior. In software-defined networks, it is far more convenient to specify the correct behavior of packets than the global behavior of the entire network. Petri nets with transits extend Petri nets and Flow-LTL extends LTL such that the data flows of tokens can be tracked. We present the tool AdamMC as the first model checker for Petri nets with transits against Flow-LTL. We describe how AdamMC can automatically encode concurrent updates of software-defined networks as Petri nets with transits and how common network specifications can be expressed in Flow-LTL. Underlying AdamMC is a reduction to a circuit model checking problem. We introduce a new reduction method that results in tremendous performance improvements compared to a previous prototype. Thereby, AdamMC can handle software-defined networks with up to 82 switches.

Abstract The manual implementation of local controllers for autonomous agents in a distributed and concurrent setting is an ambitious and error-prune task. Synthesis algorithms, however, allow for the automatic generation of such controllers given a formal specification of the system’s goal. Recently, high-level Petri games were introduced to allow for a concise modeling technique of distributed systems with a safety objective. One way of solving these games is by a translation to low-level Petri games and applying an existing solving algorithm. In this paper we present a new solving technique for a subclass of high-level Petri games with a single uncontrollable player, a bounded number of controllable players, and a local safety objective. The technique exploits symmetries in the high-level Petri game. We report on encouraging experimental results of a prototype implementation generating the reduced state space. The results for four existing and one new benchmark family show a state space reduction by up to three orders of magnitude.