Synthesizing safe coalition strategies

Abstract

Concurrent games with a fixed number of agents have been thoroughly studied, with various solution concepts and objectives for the agents. In this paper, we consider concurrent games with an arbitrary number of agents, and study the problem of synthesizing a coalition strategy to achieve a global safety objective. The problem is non-trivial since the agents do not know a priori how many they are when they start the game. We prove that the existence of a safe arbitrary-large coalition strategy for safety objectives is a PSPACE-hard problem that can be decided in exponential space. ACM Subject ClassificationTheory of computation → Verification by model checking Keywords and phrases concurrent games; parameterized verification; strategy synthesis 1 Introduction Context. The generalisation and everyday usage of modern distributed systems call both for the verification and synthesis of algorithms or strategies running on distributed systems. Concrete examples are cloud computing, blockchain technologies, servers with multiple clients, wireless sensor networks, bio-chemical systems, or fleets of drones cooperating to achieve a common goal [10]. In their general form, these systems are not only distributed, but they may also involve an arbitrary number of agents. This explains the interest of the model-checking community both for the verification of parameterized systems [14, 8], and for the synthesis of distributed strategies [20]. Our contribution is at the crossroad of those topics.Parameterized verification. Parameterized verification refers here to the verification of systems formed of an arbitrary number of agents. Often, the precise number of agents is unknown, yet, algorithms and protocols running on such distributed systems are designed to operate correctly independently of the number of agents. The automated verification and control of crowds, i.e. in case the agents are anonymous, is challenging. Remarkably, subtle changes, such as the presence or absence of a controller in the system, can drastically alter the complexity of the verification problems [14]. In the decidable cases, the intuition that bugs appear for a small number of agents is sometimes confirmed theoretically by the existence of a cutoff property, which reduces the parameterized model checking to the verification of finitely many instances [13]. In the last 15 years, parameterised verification algorithms were successfully applied to e.g. cache coherence protocols in uniform memory access multiprocessors [12], or the core of simple reliable broadcast protocols in asynchronous systems [16]. When agents have unique identifiers, most verification problems become undecidable, especially if one can use identifiers in the code agents execute [3].To our knowledge, there are few works on controlling parameterized systems. Exceptions are, control strategies for (probabilistic) broadcast networks [6] and for crowds of (probabilistic) automata [5,17,11].Distributed synthesis. The problem of distributed synthesis asks whether strategies for individual agen...