Abstract
We develop a logic-based framework for formal specification and algorithmic verification of homogeneous and dynamic concurrent multi-agent transition systems. Homogeneity means that all agents have the same available actions at any given state and the actions have the same effects regardless of which agents perform them. The state transitions are therefore determined only by the vector of numbers of agents performing each action and are specified symbolically, by means of conditions on these numbers definable in Presburger arithmetic. The agents are divided into controllable (by the system supervisor/controller) and uncontrollable, representing the environment or adversary. Dynamicity means that the numbers of controllable and uncontrollable agents may vary throughout the system evolution, possibly at every transition. As a language for formal specification we use a suitably extended version of Alternating-time Temporal Logic, where one can specify properties of the type “a coalition of (at least) n controllable agents can ensure against (at most) m uncontrollable agents that any possible evolution of the system satisfies a given objective gamma″, where gamma is specified again as a formula of that language and each of n and m is either a fixed number or a variable that can be quantified over. We provide formal semantics to our logic {mathcal {L}}_{textsc {hdmas}} and define normal form of its formulae. We then prove that every formula in {mathcal {L}}_{textsc {hdmas}} is equivalent in the finite to one in a normal form and develop an algorithm for global model checking of formulae in normal form in finite HDMAS models, which invokes model checking truth of Presburger formulae. We establish worst case complexity estimates for the model checking algorithm and illustrate it on a running example.
Highlights
1.1 The frameworkWe consider discrete concurrent multi-agent transition systems, i.e. multi-agent systems (MAS) in which the transitions take place in a discrete succession of steps, as a result of a simultaneous actions performed by all agents
The dynamicity of the systems that we consider means that the set of agents being present in the system may vary throughout the system evolution, possibly at every transition from a state to a state
As a logical language for formal specification we introduce a suitably extended version, LHDMAS, of the alternating time temporal logic (ATL)
Summary
We consider discrete concurrent multi-agent transition systems, i.e. multi-agent systems (MAS) in which the transitions take place in a discrete succession of steps, as a result of a simultaneous (or, at least mutually independent) actions performed by all agents. The dynamicity of the systems that we consider means that the set (the number) of agents being present (or, just acting) in the system may vary throughout the system evolution, possibly at every transition from a state to a state. In this work we develop a logic-based framework for formal specification and algorithmic verification of the behaviour of homogeneous dynamic multi-agent systems (hdmas) of the type described above. In particular, on scenarios where the agents are divided into controllable (by the system supervisor or controller) and uncontrollable, representing the environment or an adversary Both numbers, of controllable and uncontrollable agents, may be fixed or varying throughout the system evolution, possibly at every transition. The framework hdmas that we develop here will enable modelling the scenario above as well as specifying and algorithmically verifying claims of the kind: “The fortress
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