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.

中文翻译：

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基于逻辑的同类动态多主体系统规范和验证

我们为同构和动态并发多主体过渡系统的形式规范和算法验证开发了基于逻辑的框架。同质性意味着所有代理在任何给定状态下都具有相同的可用操作，并且这些操作具有相同的效果，而与执行这些操作的代理无关。因此，状态转换仅由执行每个操作的代理数量的向量确定，并通过在Presburger算术中可定义的关于这些数量的条件来象征性地指定。代理分为可控制的（由系统主管/控制器控制）和不可控制的，代表环境或对手。动态性意味着可控和不可控代理的数量可能会在整个系统演进过程中（可能在每次转换时）发生变化。作为正式规范的一种语言，我们使用适当的扩展版本的时态时间逻辑，其中可以指定以下类型的属性：“（至少）n个可控代理的联盟可以确保（最多）m个不可控代理对任何系统的可能演化满足给定目标\（\ gamma \） ”，其中\（\ gamma \）再次指定为该语言的公式，并且n和m分别是固定数量或可以量化的变量。我们为逻辑\（{\ mathcal {L}} _ {\ textsc {hdmas}} \}提供形式语义，并定义其公式的正常形式。然后，我们证明\（{\ mathcal {L}} _ {\ textsc {hdmas}} \）中的每个公式在有限形式上都等同于一个普通形式的公式，并开发了一种算法来对普通形式的公式进行全局模型检查在有限的HDMAS模型中，该模型调用Presburger公式的模型检查真相。我们为模型检查算法建立了最坏情况下的复杂度估计，并在一个正在运行的示例中进行了说明。